在论坛找到过不少书籍， 现在作为回馈， 全部免费。 不敢说最全， 但比较全了， 如果你们有需要的书不在里面， 我也可以帮忙找在免费传上来。这个帖子主要是概率。统计的传送门：https://bbs.pinggu.org/forum.php?mod=viewthread&tid=6410487&page=1&extra=#pid51374523初等概率都是耳熟能详的几本， 其实这部分国内的书已经写得很好了，只推荐一本的话必须是大师feller的An Introduction to Probability Theory and Its Applications, Volume 1， 写的非常好，
最后一本好像是发展还是啥的， 我也没读过。

书单：
A First Course in Probability, Sheldon Ross, 8ed, Prentice Hall, 2010
An Introduction to Probability Theory and Its Applications, Volume 1
Elementary Probability Theory    Chung
Introduction to Probability     Bertsekas and  Tsitsiklis
The Essentials of Probability     Durrett
Probability Theory  The Logic of Science




几本中等难度的：介于测度与 古典概率之间， 都比较好理解
A Probability Path   Resnick
A Second Course in Probability   Sheldon Ross
Probability    Karr
Probability and Random Processes  Grimmett


高等概率论还是要推荐下feller的volume2， 很多别的书都把他作为reference， 一些证明和topic在同类书中没有，强烈推荐。再在其他里选一本自己喜欢的就好，比如chung  K. B. Athreya, S. N. Lahiri的都很好。
书单：
An Introduction to Probability Theory and Its Applications, Volume 2
A Course in Probability Theory  Chung
Convergence of Probability Measures
Foundations of Modern Probability
Integration and Probability
Probability Theory  Loeve
Probability  Shiryaev
Measure Theory and Probability Theory (K. B. Athreya, S. N. Lahiri)
Probability and Measure 3rd Edition    Patrick Billingsley
Probability Theory and Examples  Durrett
Probability via Expectation
Probability with Martingales  Williams
Real Analysis and  Probability  Dudley




概率的极限理论研究， 比较好的工具Coupling 还有 Stein's method:

A Short Introductionto Stein's Method
An Introduction to Stein's Method
Approximate Computation of Expectations the Canonical Stein Operator.
Normal Approximation by Stein’s Method
STEIN COUPLINGS FOR NORMAL APPROXIMATION
Stein’s Method Expository Lectures and Applications



随机过程：Grimmett的Probability and Random Processes  在学高等概率之前读也非常适合，严格的数学写法， 内容例子详尽，习题很丰富 还配有一本答案：One Thousand Exercises in Probability。 随机过程部分也很好，推荐Probability and Random Processes和Adventures in Stochastic Processes 。
书单：
A First Course in Stochastic Processes - S Karlin & H M Taylor (AP, 1975)
A Second Course in Stochastic Processes  Karlin,Taylor
Adventures in Stochastic Processes  Resnick
An Introduction to Markov Processes
An Introduction to Stochastic Modelling Karlin & Taylor
Introduction to Probability Models Sheldon M.Ross 10th Edition
Introduction to stochastic processes (Lawler)
Markov Chains Gibbs Fields, Monte Carlo Simulation, and Queues
Probability and Random Processes  Grimmett
One Thousand Exercises in Probability
Stochastic Processes  Doob
Stochastic Processes Emanuel Parzen





Stochastic Analysis: 入门用Introduction to Stochastic Calculus with Applications和Stochastic Differential Equations  都行。 再深的还没读过， 没法推荐。
书单：
Brownian Motion and Stochastic Calculus  Karatzas and Shreve
Brownian Motion, Martingales, and Stochastic Calculus
Continuous Martingales and Brownian Motion  Revuz
Diffusions,Markov Processes and Martingales Volume 1
Diffusions,Markov Processes and Martingales Volume 2
Introduction to Stochastic Calculus with Applications
Lévy Processes and Stochastic Calculus
PDE and Martingale Methods in Option Pricing
Stochastic Calculus for Finance I＆II
Stochastic Differential Equations  Oksendal