强悍书单：概率与测度论+数理统计+随机过程+金融

痛定思痛。 2022-08-20 07:15 6570阅读 0赞

非数学专业 本科生

概率统计随机过程  
概率论与数理统计(第4版) 盛骤 考研必备  
概率论与数理统计教程(第2版) 茆诗松  
概率论与数理统计 陈希孺   
概率论基础教程(第8版) 罗斯、郑忠国译（已经出第9版，也是最后一版）第7版答案[http://www.docin.com/p-109941348.html][http_www.docin.com_p-109941348.html]  
概率论与数理统计(第3版改编版) 德格奥特、 谢尔维斯  
概率统计(英文版第4版）德格鲁特、舍维什  
概率与统计(英文版)Ronald E.Walpole;Raymond H.Myers;Sharon L.Myers;Keying Ye   
 概率论(英文版) 皮特曼  
应用随机过程:概率模型导论(第10版) 罗斯、龚光鲁译  
概率、统计与随机过程(第4版)(英文版) 亨利斯塔克(Henry Stark)、   
Schaum's Outlines - Probability, Random Variables And Random Processes  
Schaum's Easy Outline of Probability and Statistics.  
Schaum's Outline of Beginning Statistics, 2 Edition  
Schaum's Outlines - Elements of Statistics I - Descriptive Statistics and Probability  
Schaum's Outlines - Elements of Statistics II - Inferential Statistics  
Applied Multivariate Statistical Analysis (6th Ed)RICHARD A. JOHNSON   
Multivariate Data Analysis (7th Edition) Joseph F. Hair, William C. Black, Barry J. Babin, Rolph E. Anderson  
A Modern Introduction to Probability and Statistics\_Understanding Why and How Dekking  
Chris Spatz, "Basic Statistics: Tales of Distributions (10th edition)"  
Basic Concepts of Probability and Statistics (Classics in Applied Mathematics) by J. L. Hodges Jr and E. L. Lehmann (Jan 11, 2005)  
Modern Mathematical Statistics with Applications (Springer Texts in Statistics) by Jay L. Devore and Kenneth N. Berk (8 Dec 2011)  
A Course in Mathematical Statistics, Third Edition, Third Edition by George G. Roussas (Feb 15, 2014)  
**辅导书**  
概率论与数理统计教程:习题与解答(第2版) 茆诗松  
概率论与数理统计习题全解指南(浙大•第4版) 盛骤  
Schaum's Outline of Theory and Problems of Probability and Statistics  
  
**应用统计学**  
Elements of Statistics 6ed，Arthur L Bowley 世界上第一本统计学教材 1911  
统计学，David Freedman等著，魏宗舒，施锡铨等译 中国统计出版社 （据说是统计思想讲得最好的一本书，读了部分章节，受益很多。整本书几乎没有公式，但是讲到了统计思想的精髓。）  
Mind on statistics(英文版）， 机械工业出版社 （只需要高中的数学水平，统计的扫盲书。有一句话影响很深：Mathematics as to statistics is something like hammer, nails, wood as to a house, it's just the material and tools but not the house itself。）   
数理统计与数据分析（原书第3版）机械工业出版社 （看了就发现和国内的数理统计树有明显的不同。这本书理念很好，讲了很多新的东西，把很热门的Bootstrap方法和传统统计在一起讲了。Amazon上有书评。）  
Business Statistics a decision making approach（影印版）中国统计出版社（在实务中很实用的东西，虽然往往为数理统计的老师所不屑）  
Understanding Statistics in the behavioral science（影印版） 中国统计出版社 （和上面那本是一个系列的。老外的书都挺有意思的）  
探索性数据分析，中国统计出版社（和第一本是一个系列的。大家好好看看陈希儒老先生做的序，可以说是对中国数理统计的一种反思）   
商务与经济统计（原书第11版）安德森(Anderson D R.）等（会代数就读得懂这本书，美国最畅销的商务统计著作）   
统计学(原书第5版) 门登霍尔(William Mendenhall)、辛塞奇(Terry Sincich)  
统计模型：理论和实践（原书第2版） 弗里曼(David A.Freedman)、   
Introduction to the Theory of Statistics 14ed, George Udny Yule and Sir Maurice Kendall   
Introduction to the Theory of Statistics 3rd Edition by Alexander M. Mooda  
Introductory Statistics, Third Edition. Sheldon Ross.  
Chris Spatz, Basic Statistics: Tales of Distributions (10th edition)  
Statistics in Plain English, 3rd Edition,Timothy C. Urdan   
Theodore Coladarci, Casey Cobb, "Fundamentals of Statistical Reasoning in Education (4th Edition)  
Applied Statistics for Business and Management using Microsoft Excel by Linda Herkenhoff and John Fogli (Jan 16, 2014)  
Data Analysis: Statistical and Computational Methods for Scientists and Engineers.4th ed. 2014 edition Siegmund Brandt

**-------------------------------------------------------------------------------  
  
数学专业 （本科，研究生）**  
       一般人们对概率论这门学科的理解可以划分为三个层次：  
1古典型，未受过任何相关训练的人都属于此类，只能够理解一些离散的（古典的）概率模型；  
2近代型，通常指学过概率论基础的，从微积分的角度理解各种连续分布，概率模型的数字特征；  
3现代型，抽象地从测度论和实分析高度理解，建立在测度基础上的概率论通常所谓的高等概率论。

选一本适合自己的好的教材对自己以后的学习是决定性的重要--这是学数学的人首先必须明白的--不仅是对概率方向，对数学的各个分支都是如此。大一的时候齐名友老师跟我特别提到过这一点，可惜我当时不以为然，结果走了很多弯路，到研究生以后才慢慢明白这个道理。 **一本山寨小学校的老师七拼八凑编写的烂书，常常对学习（特别是自学）不仅无益反而有害，因为你往往浪费了时间却只能得到这个一些支离破碎的印象，这样你会遗忘得很快，很可能到头来你还得重新学一遍** ；另一些时候，你选择了众人推荐的名著，但你如果当前的水平达不到一定的层次，它往往会打击你的信心让你灰心丧气，甚至会让你不再有学下去的欲望。这两种情形显然都是人们应该尽量避免的。

需要指出的是，有的书适合作教材，有的书却只适合作参考书；就算都是教材，它定位的读者群体也可能不一样。每个人都应该根据自己的实际情况做出选择。一般好书大多都是国外的，所以如果有可能最好去看国外的原版书，就算没有这个能力也应该去锻炼这个能力。读原版书其实没看起来的那么难，你不需要懂得任何高深的语法，记熟100个单词/词组就能轻易上手，记熟300个你就能在大多数情况下不需要字典了。我记得我法语学了不到一年就来到法国读书，老师上课基本听不懂，只能自己找书看，而图书馆里绝大多数参考书都是法语的（当时不知道在网上找书）。按说我当时法语应该比大多数中国大学生英语要远差，但我抱着一本法语的拓扑书回家一边查字典一边看，两三天就完全适应了。真正看外文原版书，要克服的首要困难永远都是数学本身，而不是生词或者语法。

我推荐的学习方法是这样的：**读一本简单而直观的入门书，这样能比较容易地把握一个领域的主干，明白它要达到哪些目的，通过什么样的方法，关键性的定理有哪些；等掌握大体框架之后再找一本详尽而严密的教材慢慢推敲其细节**。中文的书我没什么好推荐的--在国内的时候看的书质量都不高（当时抱着一本书就看，对好书和烂书也没有概念）而出国之后就没再看过中文书了。我依稀记得汪嘉冈的《现代概率基础》还不错，其它的我就不知道了。对于外文书，我倒是有很多可以推荐。这样我首先要推荐的是David Williams写的Probability with martingales。书写得很薄，严格意义上说它不是一本教材，但完全可以把它当做现代概率论和鞅理论的入门书来看。我觉得很少有书能够写得象它那样把严密性，直观性以及趣味性完美的融合到一起，并且自成体系(即所谓self-contained，就是说你不需要一边看这本书一边在别的书里寻找相关定理，定义或者其它背景知识)。它只引入对主题有帮助的概念，因此这样读者就可以不必顾及细枝末节从而能够快速领悟其精髓。等你入门之后，可以看的进阶级书就很多了，比如Chung Kai Lai的A course in probability theory。

测度论的基础对于高等概率以及随机过程的学习无疑是很重要的，尽管刚开始的时候你完全可以跳过许多内容（单调类定理，测度的扩张定理，radon-nikodym定理等），但真正想把这个方向学好的人最后一定还是得回头啃这些相对枯燥的基础知识。我看过严加安的《测度论讲义》和halmos的测度论，个人感觉后者更友善些，并且更适合自学。严的书里，开篇就罗列一大串定义：什么是pi类，半环，半代数，sigma代数，单调类，lamda类，再罗列它们的一些性质，诸如a推b，b推c，c推d，d推a之类，我以为这样不容易让人抓住重点。测度论理真正重要的集类首先是sigma代数和pi类，然后是单调类和代数，其它的集类不知道也罢。

看书除了看教材，当然还得找几本参考书以备不时之需。剑桥出的Grimmett和Stirzaker合著的probability and random process，其特点是例子和习题详尽而丰富，从经典的概率论逐步过度到现代的测度空间。它虽然名为本科生教材，但我觉得其内容之丰富使其作为阶段性的参考资料已经绰绰有余了。然后是大名鼎鼎的Feller的两本An introduction to probability theory，公认的经典。其特点是通过大量的实例讲叙了许多概率论和随机过程在现实中的应用，以及各种概率模型的由来及其推导，据说适合从本科生到博士生的一切人群。但feller的书写成已经有半个世纪之久，因此一些内容还是显得太陈旧了。想看更现代一点的参考书的话，我推荐Kallenberg的Foundations of modern probability。这是一本很新的书，也是一本名副其实的参考书--因为它只能作参考书--仅600页竟然就讲完了概率论各个大大小小分支的主要内容，书里你可以找到几乎所有的重要定理，命题，及其证明。

如果你能把书基本看懂，那你已经可以算差不多入门了；如果你能闭着眼睛说出任何一个定理的证明思路，那么恭喜你，你已经学有小成。但是仅仅看书显然是不够的，想要学得好，学得牢，无论如何你还得做一定量的相应的习题--计算题为辅，证明题为主，并且要勤于思考养成习惯。为了一道题如果你的思考时间还不到一个甚至半个就放弃而去翻答案，那么根本就不算你曾为这个问题花费过努力--事实上如果你不认真思考，那么你会觉得所有的答案，所有的证明都只不过是理所当然的，trivial的，从而你也不会领悟到真谛。

上面的文字源于[http://blog.sina.com.cn/s/blog\_63ea03bc0100glad.html][http_blog.sina.com.cn_s_blog_63ea03bc0100glad.html]  
       类似的数理统计也可以按照类似的方法

严格的数理统计理论，既包含Statistical Inference（Point Estimation, Hypothesis Testing，以及Confidence Set），又包括Statistical Decision Theory；既包含Frequentist方法，又包括Bayesian的方法；既有小样本的Evaluation标准，像是 Unbiased，UMVUE等等，又包括大样本的Asymptotic Efficiency统计评价方法。当然，这个课还包含很多现代统计方法的简单介绍，比如 Nonparametric，Semiparametric，Bootstrap为代表的Resampling方法。不过这里只能是简单介绍，详细的内容只能由后续课程或者通过自学（因为这些课程的开设都是跟老师的研究兴趣有关的，一个学校不一定能把所有的课都开起来）来完成。详细的课程内容我就不多说了，因为我个人觉得，凡是想做计量理论的人这门课的内容都是必然要具备的素质，起码对于现在这个年代的计量理论来说我觉得是这样，看看现在 Econometrica，Econometric Theory，Journal of Econometrics上的Paper，基本上都是各种各样的新的Estimation，Hypothesis Testing方法的提出，所用的工具无不是基于现代数理统计最新的研究进展，如果不能打一下一个很坚固的数理统计基础，起码对我来说真是难以想象怎么来做研究将来。

这门课的主要教材就是著名的《Theory of Point Estimation》（TPE） by Lehmann and Casella，与《Testing Statistical Hypotheses》（TSH）by Lehmann and Romano，我想这两本教材的难度很多人都早就听说过了，反正我觉得这两本书真是得至少花一年的时间才能学好，课后的习题多，质量也好，这边的图书馆里能借到他们第一版的习题解答，非常老了，感觉字体很象是手写然后复印的。这本习题解答的作者一说大家肯定知道，就是写了类似于Probability百科全书的《Modern Theory of Probability》的Kallenberger了。跟这两本书难度差不多相当的Bayesian统计的书可以参考《Statistical Decision Theory and Bayesian Analysis》by Berger，注意这个Berger跟与Casella写《Statistical Inference》的Berger可不是一个人。另外，Shao Jun的《Mathematical Statistics》写的也是非常之好，内容涵盖了TPE跟TSH的所有内容几乎，当然程度要容易的多，并且这本书简单介绍了包括 Nonparametric，Semiparametric，Bootstrap，甚至还有Empirical Likelihood的几乎所有的现代统计方法，真是一书在手，天下事尽知啊。还值得一提的是，这本书习题也是很丰富，而且还有专门的一本习题答案，以供大家参考，如果能好好利用这些习题，还是那句话，受益终生。我自己上课时老师把这基本都列为了参考教材，我则除了TPE跟TSH上老师上课讲的内容外，仔细读了Shao Jun的相关内容，并且做了上面的一小部分题目，收获颇丰。Shao先生（我不知道是不是邵，所以只好写拼音）好像是国内华东师大毕业的，

现在为U of Wisconsin at Madison统计系的主任，那里Statistics PHD第一年的Math Stat Core Squence就是讲他这本书。

不知道为什么纯数学的书国内有影印版的非常多，但是统计的书国内很少找到影印版，这使我想起了有位统计牛人在一个报告上说的，国内跟国外在统计学研究上的差距这几年非但没有缩小，某种程度上反而有点扩大了。我不是做数理统计的，也不知道事实是否如此，不过统计方面影印书的出版比纯数学方面的差了很多，这是一个很奇怪的现象，因为统计在现实中的应用应该更多些，按说统计书的引进应该是更快一步才对，现在反而是相反的。这里想推荐一本中文的高等数理统计教材，那就是陈希儒先生的《高等数理统计》了，陈老的地位以及水平我想我不需要多说了，他这本书写的是非常之好，基本跟TPE，TSH差不多一个难度水平，不过就是内容少了一点。还有就是这本书习题令人称赞，而且书的后半部分就是习题的参考答案，供大家研习之用。陈老对做习题以掌握内容，训练基本技能的说法我想很多同学都是见过的，不得不说，姜还是老的辣啊！！！

个人建议：这门课值得好好花一年的时间学好TPE，TSH或者学好Shao Jun，Bayesian的部分可以参考下Berger。Berger的书国内有影印版，其他基本好像没有，不过可以找得到电子版，而且国内一些学校也有复印版。题目要认真做，多做。

上面的文字源于 [http://blog.renren.com/share/300522404/3688896622][http_blog.renren.com_share_300522404_3688896622]

下面数学专业的书才是重头戏 ,每个类目里面是该方向的第1本书  
  
概率论：**骨灰级**  
Théorie analytique des probabilités,Laplace,1812  
Calcul des probabilités by Henri Poincaré , 1912 2ed  
Calcul des probabilités, 1925 ,Paul Lévy   
Theory of probability by William Burnside, Cambridge University Press, 1928  
Introduction to mathematical probability, Uspensky,1937  
前面4本是骨灰级别的书，下面的才是近代的  
  
概率论：初**中等**   
Random Variables and Probability Distributions 3th [Harald Cramér][Harald Cram_r]  
The elements of probability theory and some of its application 2ed [Harald Cramér  
][Harald Cram_r]Mathematical Methods of Statistics: Harald Cramér  
Theory of Probability 6th Edition \[概率论教程（苏）格涅坚科（Б.В.Гнеднко）著；丁寿田译2ed\]  
De Finetti, B. (1974,5), Theory of Probability (two volumes), John Wiley & Sons.

概率论基础(第3版) 李贤平(有辅导书，这本书可以说是“抄”Gnedenko的概率论，两本书的框架几乎一样  )   
初等概率论(第4版)(英文版) 钟开莱  
概率论及其应用 第1卷 (第3版)威廉·费勒（有辅导书）  
概率论（第2版）苏淳  
概率论及数理统计(上)(第4版)邓集贤**（有辅导书）  
Probability and Random Processes 3rd ed - G. Grimmett, D. Stirzaker（有辅导书）**  
概率与信息 （苏）雅格洛姆（А.М.Яглом）  
Theory of Probability 3rd ed. H.Jeffreys  
Stochastics - Introduction to Probability and Statistics,Hans-Otto Georgii  
Probability Via Expectation(Whittle)(Expectations as the starting point for the development of probability theory; similar to my approach. Very clear. )  
JY.Ouvrard,Probabilites Tome 1 (Licence Capes)  
 Pierre Brémaud,Initiation aux probabilités et aux chaînes de Markov (2ème édition entièrement revisitée)  书后有习题解答  
Dominique Foata,Calcul des probabilités - 3e édition - Cours, exercices et problèmes corrigés 书后有习题解答   
An Intermediate Course in Probability (Allan Gut)  
Applied probability (2ed., Springer, 2010)Lange K  
Probability and Stochastic Processes \[2014\]by Ionut Florescu

**测度论（或者说偏概率论的实分析）**

Measure theory,Halmos,  
严加安 测度论讲义（第二版）  
Schilling ，Measures, Integrals and Martingales 有习题解答 [http://www.docin.com/p-750702313.html][http_www.docin.com_p-750702313.html]  
Capinski，Measure, Integral and Probability, Second Edition 书后有习题解答   
Stroock ，Essentials of Integration Theory for Analysis (Graduate Texts in Mathematics)有习题解答  
Bartle，A Modern Theory of Integration (Graduate Studies in Mathematics)书后有习题解答  
Théorie de la mesure (exercices et problèmes corrigés) de Khoan Vo Khac  
Folland, G. B. Real Analysis:Modern Techniques and Their Applications (Excellent source for measure theory and real analysis. )  
Bass,Real Analysis for Graduate Students, Second Edition  
Makarov,Real Analysis Measures, Integrals and Applications  
A Course in Real Analysis 2ed (John N. McDonald, Neil A. Weiss)  
Measure and Integration Theory (Heinz Bauer)  
Measure and Integration A Concise Introduction to Real Analysis,Leonard F. Richardson  
Measure Theory and Integration M.E.Taylor  
Measure theory, Doob  
Measure Theory I,II (V.I. Bogachev)  
Measure Theory Second Edition Donald L. Cohn  
Tao, Terence,. An introduction to measure theory. Vol. 126. AMS Bookstore, 2011.  
Theorie de la mesure et Integration: Measure Theory and Integration de Prof. Magid Maatallah (13 décembre 2010)  
Real Analysis: Theory of Measure and Integration (3rd Edition 2014) by J Yeh  
A Course on Integration Theory: including more than 150 exercises with detailed answers \[2014\]by Nicolas Lerner

**辅导书**  
Exercices corrigés en théorie de la mesure et de l'intégration de Yves Ducel et Jean-Pascal Ansel (5 mai 1998)  
J Yeh,Problems and Proofs in Real Analysis: Theory of Measure and Integration,3ed

Exercises in Analysis: Part 1 (Problem Books in Mathematics) by Leszek Gasinski and Nikolaos S. Papageorgiou (2014)

**高等**  
Kolmogorov, A. N. Foundations of the Theory of Probability \[概率论导引（苏）柯尔莫戈洛夫等著；周概容，肖慧敏译\](The original. It contains most of what goes into a modern probability course, in under a hundred pages. Hard reading, because notation and fashion have changed, but the ideas are mostly all there. Martingale theory wasn't invented in~1933, when the book first appeared. A landmark in the history of probability. "Grundbegriffe der Wahrscheinlichkeitrechnung,"' 'Ergebnisse Der Mathematik', 1933.)

Lévy,Théorie de l'addition des variables aléatoires，1937 ,1954 2ed  
M. Loeve, 'Probability Theory, I and II, 4th Edition', Springer-Verlag, New York, 1977. ( The classic text on probability ，likely the first rock solid, quite comprehensive, highly polished presentation of 'modern' probability was the first edition)Loeve是Lévy的学生

Jacques Neveu,Mathematical foundations of the calculus of probability (Holden-Day series in probability and statistics)翻译自法语Bases mathématiques du calcul des probabilités : Par Jacques Neveu de Jacques Neveu (1964)Neveu是Loeve的学生  
L. Breiman (1992), Probability. SIAM, Philadelphia.（A good book to look at after you think you know what is going on. Deceptive at times, because hard ideas are made to seem easy. Very good for weak convergence, characteristic functions, and more advanced topics. Worth owning. Breiman is the more 'practical' and 'accessible'; Neveu is a crown jewel of elegance and succinctness but not always easy to read.）1968年第1版  
概率论教程:英文版(第3版) 钟开莱(A standard text. A good place to look for standard proofs.)

概率论及其应用 第2卷(第3版)/威廉·费勒(A classic. If you are serious about probability theory you need to own this book (and the companion volume~I). Covers lots of material not found in other texts. Very good on characteristic functions; very little on martingales. Unfortunately, Feller tried to avoid measure theory. )

Howard G. Tucker, A Graduate Course in Probability, (1995)1967年第1版  
Chow.Y.S的Probability Theory: Independence, Interchangeability, Martingales 3ed 华人数学家 周元燊(Written in a technical style, but full of information. Good on martingales and exchangeability. It has useful variations on technical topics such as inequalities for sums and for martingales.)1978年第1版  
 R. G. Laha, V. K. Rohatgi,Probability theory(1979)

概率论（日）伊藤清著 刘璋温译  
概率(第1,2卷)(修订和补充第3版) 施利亚耶夫  
高等概率论及其应用 胡迪鹤  
测度与概率(第2版) 严士健  
概率论教程 第2版 缪柏其，胡太忠  
测度论与概率论基础(程士宏) 书后有习题解答  
现代概率论基础\_第二版\_汪嘉冈  
高等概率论与随机过程（龚兆仁）书后有习题解答   
はじめての確率論 測度から確率へ，佐藤 坦  
Kallenberg的Foundations of modern probability 2ed (Quoting an amazon.com reviewer: \`\`.... a compendium of all the relevant results of probability ..... similar in breadth and depth to Loeve's classical text of the mid 70's. It is not suited as a textbook, as it lacks the many examples that are needed to absorb the theory at a first pass. It works best as a reference book or a "second pass" textbook.")

David Williams的Probability with martingales(A tad eccentric, but superbly clear. An author who conveys his enthusiasm for a great subject.  Concise treatment emphasizes usefulness of martingales. )

Sheldon M Ross,A Second Course in Probability   
R. Durrett,Probability Theory and Examples 4th edition有习题解答  
**Billingsley的Probability and Measure 3rd Edition （**Very well written. Particularly recommended for the discussion on conditioning. Covers many topics .）

**Athreya的Measure Theory And Probability Theory **

**Erhan Cnlar,GTM261.Probability and Stochastics **  
**Malliavin.P,GTM157.Integration.and.Probability **有习题解答   
**A. Rény,Foundations of Probability**  
Jacod J,Probability Essentials （法国教材，只有200多页，特别适用于经济学方向，网上有答案）  
Probability Theory (1996) Heinz Bauer  
Probability for Statisticians (Galen R. Shorack)  
Measures and Probabilities (Universitext) \[Michel Simonnet, C.-M. Marle\]  
Resnick, S., A Probability Path, Birkhäuser. 有习题解答   
Janos Galambos,Advanced Probability Theory,Second Edition书后有习题解答   
Fristedt. A modern approach to probability theory. 1997.有习题解答   
Klenke，Probability Theory - A Comprehensive Course 2ed，2013  
A basic course in probability theory（不到200页的，高等概率论教材，短小精悍）  
J.C. Taylor (1997), An introduction to measure and probability. Springer,

Probability Theory(Universitext) ,Borovkov, Alexandr A. 2013,Springer ,  
Probability: A Graduate Course [Allan Gut][] 2013,Springer  
Probability(Davar. Khoshnevisan)GSM080  
A First Look at Rigorous Probability Theory, 2ed (Jeffrey S. Rosenthal)  
Real Analysis and Probability.DUDLEY (A thorough text that has become one of my favourites. Read the notes at the end of each chapter to see how a real scholar works. Highly recommended)

Theory of Probability and Random Processes (Leonid B. Koralov, Yakov G. Sinai).

Ash, R. B. Real Analysis and Probability (Good background on measure theory, particularly the connections between topology and measure. Recommended for martingales and conditioning.)书后有习题解答   
Philippe Barbé, Michel Ledoux, Probabilité,2007 (有习题解答书)  
Modèles aléatoires et physique probabiliste (French Edition) by Franck Jedrzejewski 现代概率论在物理中的应用

Probability for Statistics and Machine Learning Fundamentals and Advanced Topics ,Gupta   
Fundamentals of Probability A First Course  Gupta  
A User's Guide to Measure Theoretic Probability , Pollard   
Theory of Probability and Random Processes, Leonid Koralov，Yakov G. Sinai F  
A Graduate Course in Probability and Statistics Vol.1 Essentials of Probability for Statistics \[Hung T.Nguyen;Tonghui Wang\]  
The Theory of Probability: Explorations and Applications, Venkatesh   
Advanced Probability Theory(荆炳义 高等概率讲义)  
Probability Tools with Examples 2013-2014-UCSD Lecture Notes，Bruce K. Driver.  [http://www.docin.com/p-753247528.html][http_www.docin.com_p-753247528.html]

Probability Theory S.R.S.Varadhan(Courant Lecture Notes)[http://www.docin.com/p-753247669.html][http_www.docin.com_p-753247669.html]  
Theorie de la Mesure et Probabilités: Measure Theory and Probability (avec exercices et problèmes corrigés) de Magid Maatallah (27 août 2010)

Probabilites Tome 2 (Master Agregation) JY.Ouvrard

Walsh, J. (2012), Knowing the Odds: An Introduction to Probability, AMS.  
Mathematics of Probability (Graduate Studies in Mathematics) by Daniel W. Stroock   
Théorie des probabilités. Une introduction élémentaire. de Bernard Candelpergher (14 mars 2013)  
Théorie de la Mesure et de l'Intégration pour les Probabilités Cours & Exercices Corrigés de Maryse Béguin (25 juin 2013)书后有习题解答  
Probability Theory in Finance: A Mathematical Guide to the Black-scholes Formula (Graduate Studies in Mathematics)书后有习题解答  
Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach by Guojun Gan, Chaoqun Ma and Hong Xie 2014  
An Introduction to Measure-theoretic Probability, Second Edition by George G. Roussas (Apr 15, 2014)

Probability: The Classical Limit Theorems Hardcover, 2014 by Henry McKean

辅导书  
Schaum's Outlines - Probability, Random Variables And Random Processes  
概率论基础学习指导书 李贤平 陈子毅  
[概率论题解1000例(英文版)][1000] G.格里梅特、D.斯特扎克  
[概率论习题集][Link 1]施利亚耶夫、 苏淳译概率论题解（英文版）  
T.M.Mills,Problems in Probability  
Probabilites: cours et problemes,Lipschutz\_S.  
Probability through problem, Capinski  
Exercises in Probability: A Guided Tour from Measure Theory to Random Processes，L. Chaumont and M. Yor  
Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions ,A. A. Sveshnikov   
Theoretical Exercises in Probability and Statistics, 2nd Edition  
Hervé Carrieu,Probabilité : Exercices corrigés de Hervé Carrieu , 2008

W.Feller 第1卷 概率论及其应用题解 陈希孺  
王道益，分析概率论与随机过程习题解析（包含了胡迪鹤写的分析概率和随机过程的习题解答）  
概率论教程题解,北京化工学院数学教研室（Gnedenko概率论的习题解答）  
概率论习题集 （苏）Л.Д.梅沙尔金著；盛骤等译  
概率论习题集（苏）特罗高夫切夫等著；何声武等译  
概率论题解 蔡焉 杨守昌(复旦大学概率论第1卷的答案，也就是李贤平概率论基础的第1版，概率论基础学习指导书的前生)

数理统计：中等  
Mathematical Methods of Statistics: [Harald Cramér  
 ][Harald Cram_r]Kendall's Advanced Theory of Statistics  v2,3 第2卷讲统计推断 第3卷讲实验设计与时间序列 （第3版有辅导书）  
Mathematical Statistics Van der Waerden B. L 1969  
Mathematical Statistics: A Decision Theoretic Approach \[Thomas S. Ferguson\] 1976 网上有习题解答[http://www.docin.com/p-771396804.html][http_www.docin.com_p-771396804.html]  
数理统计学教程 陈希孺    
数理统计学讲义 陈家鼎 解答[http://www.docin.com/p-437425905.html][http_www.docin.com_p-437425905.html]  
Mathematical Statistics :Basic Ideas and Selected Topics(接近测度论语言，1版有中文辅导书，第2版分了2卷，第一卷出版了，第二卷据作者说2013年出版)  
V.K.Rohatgi的An Introduction to Probability Theory and Mathematical Statistics   
Stochastics - Introduction to Probability and Statistics,Hans-Otto Georgii  
Introduction to Mathematical Statistics, 7th edition, Hogg, McKean, Craig, 2013（第4版有辅导书，第6版网上有习题解答）

数理统计,韦来生  
 Pestman,Wiebe R的Mathematical Statistics 有辅导书  
[概率论及数理统计(下册)(第4版)][4]邓集贤（有辅导书）  
Samuel S. Wilks的Mathematical Statistics  
Rao C.R. 的Linear Statistical Inference and its applications 2ed([倪国熙][Link 2]，[陈希孺][Link 3]写了这本书的部分参考答案)  
All of Statistics - A Concise Course in Statistical Inference - Larry Wasserman  
TheoreticalStatistics, D. R. Cox,D.V. Hinkley（有辅导书）  
Boos,Essential Statistical Inference Theory and Methods.2013   
StatisticalInference, 2nd edition, by George Casella [http://www.docin.com/p-757409493.html ][http_www.docin.com_p-757409493.html];网上有习题解答

Modern Mathematical Statistics with Applications Devore,.Berk,.2ed 2012  
Abramovich,Statistical Theory: A Concise Introduction (Chapman & Hall/CRC Texts in Statistical Science) \[2013\]书后有习题解答

数理统计：高等  
 Lehmann,Testing Statistical Hypotheses.3ed(有习题解答)  
Lehmann,Theory of Point Estimation.2ed  
Lehmann,Elements of Large-sample Theory  
Lehmann, Nonparametrics: statistical methods based on ranks（书后有部分计算题的解答，以上是Lehmann统计学的四部曲）   
Jun Shao  Mathematical Statistics (2nd ed.)   
数理统计引论 陈希孺  
高等数理统计 陈希孺（习题解答占了书的一半）  
高等数理统计(第2版) 茆诗松  
高等统计学，郑忠国、童行伟、 赵慧 书后有习题解答   
Mathematical Theory of Statistics:Statistical Experiments and Asymptotic Decision Theory  
Theory of Statistics 2ed Mark J. Sachervish   
Advanced Statistics: Volume 1: Description of Populations ,Shelby J. Haberma  
A Graduate Course in Probability and Statistics.Volume II:Essentials of Statistics,Hung T.Nguyen;Tonghui Wang  
Abstract Inference ,[Grenander U.][]   
現代数理統計学, 竹村 彰通  
Mathematical statistics,Borovkov, Alexandr A.   
Theoretical Statistics: Topics for a Core Course  Robert W. Keener （书后有解答，适合数学专业统计学研究生课程使用，是2010年Springer出版社刚出版书。密歇根大学教授，他同时是Institute of Mathematical Statistics的fellow）   
Korostelev Mathematical Statistics: Asymptotic Minimax Theory   
Advanced Mathematical Statistics I(荆炳义 高等统计学讲义)  
Wahrscheinlichkeitstheorie und Stochastische Prozesse (Springer-Lehrbuch Masterclass)  by Michael Mürmann (Dec 31, 2013)  
Examples and Problems in Mathematical Statistics (Wiley Series in Probability and Statistics) - Shelemyahu Zacks,2014  
Statistical Theory and Inference, 2014 by David Olive   
 Basics of Modern Mathematical Statistics(Springer Texts in Statistics)Spokoiny, Vladimir, Dickhaus, Thorsten 2014([http://www.docin.com/p-758997042.html][http_www.docin.com_p-758997042.html]有习题解答书)  
L. Rüschendorf, Mathematische Statistik (Springer-Lehrbuch Masterclass)

**辅导书 **  
[数理统计习题教程(上下)][Link 4]李泽慧 J.Bickel 第一版解答  
Mathematical Statistics -- Exercises and Solutions，Jun Shao   
Mathematical Statistics Problems and Detailed Solutions ，Pestman, Wiebe R. Alberink, Ivo B  
数理统计学导论习题详解R.V霍格[http://www.docin.com/p-287034823.html][http_www.docin.com_p-287034823.html]  
概率论及数理统计（上下）习题解答 许刘俊  
A. A. Sveshnikov的Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions  
倪国熙，陈希孺著 线性统计与线性代数 参考资料  
Problems and solutions in theoreticalstatistics， David Roxbee Cox  
Testing statistical hypotheses : worked solutions / W.C.M. Kallenberg, et al.  
Exercises in Theoretical Statistics: With Answers and Hints on Solutions by Sir Maurice Kendall    
Problems in mathematical statistics G.Ivchenko  
Basics of Modern Mathematical Statistics: Exercises and Solutions (Springer Texts in Statistics) [Härdle][H_rdle]   
Solutions Manual to Mathematical Statistics Asymptotic Minimax Theory [http://www.docin.com/p-706903193.html][http_www.docin.com_p-706903193.html]  
Kallenberg, W. C. M. Testing statistical hypotheses : worked solutions [http://www.docin.com/p-759300376.html][http_www.docin.com_p-759300376.html]

** **  
**统计分布论（运用概率统计研究各种分布函数的性质）**  
**Kendall's Advanced Theory of Statistics  vol 1 主要讲分布论（第3版有辅导书）**  
Norman L. Johnson的Univariate Discrete Distributions, 3ed  
Kocherlakota的Bivariate Discrete Distributions  
Norman L. Johnson的Discrete Multivariate Distributions Norman   
Norman L. Johnson的Continuous Univariate Distributions, Vol. 1，2  
N. Balakrishnan的Continuous Bivariate Distributions  
Norman L. Johnson的Continuous Multivariate Distributions, Volume 1, Models and Applications, 2nd Edition  
N. BALAKRISHNAN的A Primer on Statistical Distributions (2003)  
A K Gupta Matrix Variate Distributions   
N. Balakrishnan的Advances in Distribution Theory, Order Statistics, and Inference  
统计分布,方开泰  
Charalambos A. Charalambides 的Combinatorial Methods In Discrete Distributions  
Johnson N.L, Kotz S. Urn models and their application (Wiley, 1977) 用瓮模型写的概率论  
Christian,Statistical Size Distributions in Economics and Actuarial Sciences  
Hogg, Klugman Loss Distributions   
Krishnamoorthy,Handbook of statistical distributions with applications(Taylor and Francis, 2006)  
  
**随机过程**  
J.L. Doob (1953), Stochastic processes (2nd ed.). John Wiley & Sons,  
Stochastic Processes (Emanuel Parzen)  
 Introduction to Stochastic Processes (1975) by Erhan Cinlar   
A First Course In Stochastic Processes(Karlin)  
A Second Course In Stochastic Processes(Karlin)  
Diffusions, Markov Processes, and Martingales Volume 1，2 David Williams   
Introduction to Stochastic Processes by Paul Gerhard Hoel, Sidney C. Port and Charles J. Stone

Essentials of Stochastic Processes(Durrett)  
Introduction to Probability Models, Eleventh Edition by Sheldon M. Ross (Feb 15, 2014)  
Stochastic Process.2nd.Sheldon Ross  
Stochastic Processes for Insurance and Finance，Tomasz Rolski  
R. Bhattacharya .Stochastic processes with applications. John Wiley & Sons, New York.  
S. Resnick (1992), Adventures in stochastic processes. Birkhauser, Boston.   
Basics of Applied Stochastic Processes (2010)Springer Richard Serfozo  
Bass,Stochastic Processes,2011  
Stochastic Processes Lectures Given at Aarhus University,Kyosi Ito   
Durret,Essentials of stochastic processes,2012  
Kyosi Ito ,Stochastic Processes: Lectures Given at Aarhus University,2004 书后有习题解答  
Dominique Foata, Aimé Fuchs,Processus stochastiques : Processus de poisson, chaînes de Markov et martingales,2004 书后有习题解答   
Measure theory and filtering introduction and applications 有习题解答  
Theory of Stochastic Processes: With Applications to Financial Mathematics and Risk Theory 书后有习题解答  
Understanding Markov Chains Examples and Applications 书后有习题解答  
Schilling,Brownian Motion,An Introduction to Stochastic Processes,2012 有习题解答   
随机过程 伊藤清  
随机过程论—基础、理论、应用（胡迪鹤）  
随机过程导论,Edward P.C.Kao  
随机过程论【布林斯基,施利亚耶夫】  
随机过程论 第1-3卷 И.И.基赫曼等  
随机过程通论第1-2卷(王梓坤)  
应用随机过程(林元烈)  
应用随机过程(张波张景肖)书后有习题解答  
随机模型概论(英文版.第4版)Mark A.Pinsky;Samuel Karlin  
Introduction to Stochastic Processes, Second Edition (Chapman & Hall/CRC Probability Series) by Gregory F. Lawler (May 16, 2006)  
Applied Stochastic Processes by Ming Liao (Jul 22, 2013)  
Random Processes by Example by Mikhail Lifshits (Mar 10, 2014)  
Stochastic Processes: Theory for Applications by Robert G. Gallager (Feb 28, 2014)  
Stochastische Prozesse (Mathematik Kompakt) (German Edition) by Götz Kersting and Anton Wakolbinger (Jul 29, 2014)

**辅导书**

Stochastic processes. problems and solutions, Takacz L  
Theory of Stochastic Processes: With Applications to Financial Mathematics and Risk Theory (Problem Books in Mathematics)  
Exercises in Probability: A Guided Tour from Measure Theory to Random Processes, via Conditioning.  2ed,Chaumont.    
Solution Manual of Introduction to Probability Models 10ed  
随机过程疑难分析与解题方法 孙昊、 孙清华  
随机过程习题解析(第2版) 陆传赉  
随机过程及应用习题集 张晓军

**随机分析(随机微分，积分，变分)**

Karatzas,Shreve,Brownian motion and stochastic calculus,1991 书后有习题解答

Stochastic Differential Equations 6ed 书后有习题解答Malliavin Calculus for Lévy Processes with Applications to Finance 书后有习题解答Introduction to Stochastic Calculus with Applications Fima C. Klebner  书后有习题解答  
An Introduction to Stochastic Differential Equations Lawrence C. Evans  
Measure Theory and Filtering-Introduction and Applications   
Introduction to Stochastic Integration - Second Edition Kai Lai Chung

Introduction to Stochastic Integration (Universitext) by Hui-Hsiung Kuo   
Stochastic Integration Theory (Oxford Graduate Texts in Mathematics) by Peter Medvegyev  
Stochastic Integration and Differential Equations (Stochastic Modelling and Applied Probability) by Philip E. Protter  
Stochastic Calculus: Applications in Science and Engineering by Mircea Grigoriu

Introduction To Stochastic Calculus With Applications (3rd Edition) by Fima C. Klebaner

Stochastic Analysis and Diffusion Processes (Oxford Graduate Texts in Mathematics) by Gopinath Kallianpur and P Sundar (Feb 6, 2014)

**随机金融  
Mikosch,Elementary Stochastic Calculus With Finance in View,1988 ([被引用次数：289][289])**  
 Karatzas,Shreve,Methods of mathematical finance,1998 （ [被引用次数：2110][2110] ）    
**Shiryaev,Essentials of Stochastic Finance,2000 （[被引用次数：857][857]）**  
Steele,Stochastic Calculus and Financial Applications,2001 ( [被引用次数：385][385])  
Shreve,Stochastic calculus for finance I: The binomial asset pricing model,2004 ( [被引用次数：1172][1172])有习题解答 [http://www.docin.com/p-750142388.html][http_www.docin.com_p-750142388.html]    or  [http://www.docin.com/p-750142435.html][http_www.docin.com_p-750142435.html]  
Shreve,Stochastic Calculus for Finance II, Continuous Time Models,2004 ( [被引用次数：1172][1172])有习题解答 [http://www.docin.com/p-750142402.html][http_www.docin.com_p-750142402.html]  
Benth,Option theory with stochastic analysis: an introduction to mathematical finance,2004 ( [被引用次数：49][49])  
Elliott,Mathematics of Financial Markets Second Edition,2005 （ [被引用次数：472][472]）  
史树中  [金融学中的数学][Link 5]    2006  
Lin,Introductory Stochastic Analysis for Finance and Insurance,2006 ( [被引用次数：13][13])   
Sondermann,Introduction to Stochastic Calculus for Finance: A New Didactic Approach,2006 ( [被引用次数：24][24] *The text is also useful for mathematicians interested in the methods of modern mathematical finance without prior knowledge of advanced stochastic analysis*)  
Lamberton,Introduction to stochastic calculus applied to finance,2008 ( [被引用次数：904][904])  
Kwok,Mathematical Models of Financial Derivatives Second Edition,2008 ( [被引用次数：589][589])  
Kennedy,Stochastic Financial Models ,2010 ( [被引用次数：9][9])  
Statistics of financial markets: an introduction 3ed, Jürgen Franke, Wolfgang Karl Härdle and Christian Matthias Hafner 2010( [被引用次数：188][188] )有辅导书

Ross,An Elementary introduction to Mathematical Finance 3ed ,2011 （[被引用次数：115][115]）  
Fllmer,Stochastic Finance An Introduction in Discrete Time 3ed,2011 ([被引用次数：1235][1235])  
Capinski,Mathematics for Finance An Introduction to Financial Engineering 2011 2ed ([被引用次数：112][112] 仅仅需要高数和概率统计知识 适合非数学专业)  
Večeř ,Stochastic Finance: A Numeraire Approach ,2011 ([被引用次数：7][7])  
严加安 金融数学引论 2012  
Capiński, Stochastic Calculus for Finance ,2012  
 Janssen, Mathematical Finance: Deterministic and Stochastic Models,2013 ([被引用次数：14][14])  
McCauley,Stochastic Calculus and Differential Equations for Physics and Finance,2013  
Kijima,Stochastic Processes with Applications to Finance,2013 ([被引用次数：106][106])  
Michael Mastro, Financial Derivative and Energy Market Valuation: Theory and Implementation in MATLAB  
**Stochastic Calculus and Differential Equations for Physics and Finance by Joseph L. McCauley **  
**Stochastic Finance: An Introduction with Market Examples (Chapman & Hall/CRC Financial Mathematics Series) by Nicolas Privault (Dec 20, 2013)**  
**Elements of Stochastic Finance: Theory, Methods, and Computation by Frederi G. Viens, Jose Enrique Figueroa-lopez and Alexandra Chronopoulou (2014)  
 **  
**辅导书**  
Statistics of Financial Markets: Exercises and Solutions 2ed 2013 by Szymon Borak, Wolfgang Karl Härdle and Brenda López-Cabrera (Jan 11, 2013)  
Problems and Solutions in Mathematical Finance: Volume I - Stochastic Calculus (The Wiley Finance Series) by Eric Chin, Sverrir Olafsson and Dian Nel  
Problems and Solutions in Mathematical Finance Volume II: Equity Derivatives (The Wiley Finance Series)  
Problems and Solutions in Mathematical Finance Volume III: Interest Rates and Inflation Indexed Derivatives (The Wiley Finance Series)

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（来源：数学建模与数学应用论坛，有一定改动和编加）

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