Probability and Statistical Reference
Syllabus on Probability Theory
Random variable, Expectation, Independence
Variance and covariance, correlation, moment
Various distribution functions
Multivariate distribution
Characteristic function, Generating function
Various modes of convergence of random variables
Law of large numbers
Random series
Central limit theorem
Bayes formula, Conditional probability
Conditional expectation given a sigma-field
Markov chains
References:
- Rick Durrett, Probability: Theory and Examples, Cambridge University Press, 2010
- Kai-Lai Chung , A Course in Probability Theory, New York, 1968, 有中译本(钟开莱：概率论教程， 机械工业出版社， 2010）
Syllabus on Statistics
Distribution Theory and Basic Statistics
Families of continuous distributions: normal, chi-sq, t, F, gamma, beta; Families of discrete distributions: multinomial, Poisson, negative binomial; Basic statistics: sample mean, variance, median and quantiles.
Testing
Neyman-Pearson paradigm, null and alternative hypotheses, simple and composite hypotheses, type I and type II errors, power, most powerful test, likelihood ratio test, Neyman-Pearson Theorem, generalized likelihood ratio test.
Estimation
Parameter estimation, method of moments, maximum likelihood estimation, criteria for evaluation of estimators, Fisher information and its use, confidence interval.
Bayesian Statistics
Prior, posterior, conjugate priors, Bayesian estimator.
Large sample properties
Consistency, asymptotic normality, chi-sq approximation to likelihood ratio statistic.
References:
- Casella, G. and Berger, R.L. (2002). Statistical Inference (2nd Ed.) Duxbury Press.
- 茆诗松，程依明，濮晓龙，概率论与数理统计教程（第二版），高等教育出版社，2008.
- 陈家鼎，孙山泽，李东风，刘力平，数理统计学讲义，高等教育出版社，2006.
- 郑明，陈子毅，汪嘉冈，数理统计讲义，复旦大学出版社，2006.
- 陈希孺，倪国熙，数理统计学教程，中国科学技术大学出版社，2009.
Sheldon M. Ross, Introduction to Probability Models
R. Larsen and M. Marx: An Introduction to Mathematical Statistics, Prentice-Hall, 1986。
Foundations of Modern Probability by Olav Kallenberg
汪仁官，《概率论引论》，北大版
程士宏，《高等概率论》，北大版
严士健，《概率论基础》，北大版
陈希孺，高等数理统计，科大版
王(辛/梓)坤《概率论基础及其应用》《概率论及其应用》科学出版社
苏淳《概率论》中国科学技术大学讲义
杨振明《概率论》科学出版社
《概率论基础》李贤平
《概率论与数理统计》（上、下）中山大学数学力学系编
82《概率论基础》李贤平
84《概率与统计》陈家鼎, 郑忠国编著
85《概率论与数理统计》盛骤，谢式千，潘承义编
【习题集】
【提高】
88《测度论与概率论基础》程士宏编著
90《现代概率论基础》汪嘉冈编著
91《分析概率论》拉普拉斯著
《决疑数学》（伽罗威著），
92《概率论及其应用》威廉•费勒著
93《概率， 随机变量， 与随机过程》 帕普里斯著
94《概率论与数理统计讲义•提高篇》姚孟臣编著
95《概率论思维论》张德然著
96《概率论思想方法的历史研究》朱春浩编著
97《概率论的思想与方法》运怀立著
补充：《逻辑代数》沈小丰, 喻兰, 沈钰编著
Random Walk & Random Variables
Hughes, B. Random Walks and Random Environments. Vol. 1. Oxford, UK: Clarendon Press, 1996. ISBN: 0198537883.
Buy at Amazon Redner, S. A Guide to First Passage Processes. Cambridge, UK: Cambridge University Press, 2001. ISBN: 0521652480.
Buy at Amazon Risken, H. The Fokker-Planck Equation. 2nd ed. New York, NY: Springer-Verlag, 1989. ISBN: 0387504982.
Further Readings
Buy at Amazon Bouchaud, J. P., and M. Potters. Theory of Financial Risks. Cambridge, UK: Cambridge University Press, 2000. ISBN: 0521782325.
Buy at Amazon Crank, J. Mathematics of Diffusion. 2nd ed. Oxford, UK: Clarendon Press, 1975. ISBN: 0198533446.
Buy at Amazon Rudnick, J., and G. Gaspari. Elements of the Random Walk. Cambridge, UK: Cambridge University Press, 2004. ISBN: 0521828910.
Buy at Amazon Spitzer, F. Principles of the Random Walk. 2nd ed. New York, NY: Springer-Verlag, 2001. ISBN: 0387951547.
Stochastic Calculus & Stochastic Process
S.M. Ross, Stochastic Processes, John Wiley & Sons, 1983
A First Course in Stochastic Processes by Samuel Karlin, Howard Taylor
A Second Course in Stochastic Processes by Samuel Karlin, Howard Taylor
The Theory of Stochastic Processes I &II Gikhman, I.I., Skorokhod, A.V
《随机过程及应用》陆大金
《随机过程》孙洪祥
《随机过程论》钱敏平，龚鲁光
钱敏平，龚光鲁，随机过程，北京大学出版社
钱敏平，龚光鲁，随机微分方程，北京大学出版社
Probabilistic Methods in Combinatorics
The Probabilistic Method, by N. Alon and J. H. Spencer, 3rd Edition, Wiley, 2008.
Probability and Statistical Reference
Syllabus on Probability Theory
Random variable, Expectation, Independence
Variance and covariance, correlation, moment
Various distribution functions
Multivariate distribution
Characteristic function, Generating function
Various modes of convergence of random variables
Law of large numbers
Random series
Central limit theorem
Bayes formula, Conditional probability
Conditional expectation given a sigma-field
Markov chains
References:
1. Rick Durrett, Probability: Theory and Examples, Cambridge University Press, 2010
2. Kai-Lai Chung , A Course in Probability Theory, New York, 1968, Chinese translation ( Zhong Kailai: course in probability theory,mechanical industry publishing house, 2010)
Syllabus on Statistics
Distribution Theory and Basic Statistics
Families of continuous distributions: normal, chi-sq, t, F, gamma, beta; Families of discrete distributions: multinomial, Poisson, negative binomial; Basic statistics: sample mean, variance, median and quantiles.
Testing
Neyman-Pearson paradigm, null and alternative hypotheses, simple and composite hypotheses, type I and type II errors, power, most powerful test, likelihood ratio test, Neyman-Pearson Theorem , generalized likelihood ratio test.
Estimation
Parameter estimation, method of moments, maximum likelihood estimation, criteria for evaluation of estimators, Fisher information and its use, confidence interval.
Bayesian Statistics
Prior, posterior, conjugate priors, Bayesian estimator.
Large sample properties
Consistency, asymptotic normality, chi-sq approximation to likelihood ratio statistic.
References:
3. Casella, G. and Berger, R.L. (2002). Statistical Inference (2nd Ed.) Duxbury Press.
4. Mao poem song, Cheng Yiming, Pu Xiaolong, probability theory and mathematical statistics course (Second Edition), higher education press2008.
5. Chen Jiading, Sun Shanze, Li Dongfeng and Liu Liping, lectures on mathematical statistics, higher education press 2006.
6. Cheng, Chen Ziyi, Wang Jiagang, mathematical statistics, handouts, Fudan University Press 2006.
7. Chen xiru, Ni Guoxi, course in mathematical statistics, China University of science and technology press, 2009.
Sheldon M. Ross, Introduction to Probability Models
R. Larsen and M. Marx: An Introduction to Mathematical Statistics, Prentice-Hall, 1986。
Foundations of Modern Probability by Olav Kallenberg
Wang ren, an introduction to probability theory, North Edition
CHENG Shihong, the high probability of Peking University
Yan Shijian, of the probability theory Foundation of the North version
Chen xiru, higher mathematics and statistics, University
Wang ( Xin / Zi ) Kun of the Foundation and its application to probability theory, probability theory and its applications, science press
Su Chun of the probability of the China Science and Technology University lecture notes
Yang Zhenming probability theory science press
Of the probability theory Foundation of the Li Xianping
Probability theory and mathematical statistics (upper and lower) of Sun Yat-sen University Department of mathematics and mechanics of knitting
82 Of the probability theory Foundation of the Li Xianping
84 Chen Jiading of the probability and statistics , Written by Zheng Zhongguo
85 Sudden sheng of the probability theory and mathematical statistics, Xie shiqian, Pan Chengyi series
“Onward”
“Increase”
88 Written by CHENG Shihong of the measure theory and probability theory
90 Of the basis of modern probability theory written by Wang Jiagang
91 The analysis of probability theory, Laplacian of the
Solve math (Galen Lowe with),
92 Weilian·feile of the probability theory and its applications
93 The probability, Random variables, and stochastic processes papulisi the
94 Lectures on probability theory and mathematical statistics: lower post Yao Mengchen authoring
95 Probability theory thinking of the theory of Zhang Deran with
96 The probability theory thinking history study written by Zhu Chunhao
97 Shipped huaili of probability theory and method of the
Added: the logical algebra Shen Xiaofeng , Yu Lan , Written by Shen Yu
Random Walk & Random Variables
Hughes, B. Random Walks and Random Environments. Vol. 1. Oxford, UK: Clarendon Press, 1996. ISBN: 0198537883.
Buy at Amazon Redner, S. A Guide to First Passage Processes. Cambridge, UK: Cambridge University Press, 2001. ISBN: 0521652480.
Buy at Amazon Risken, H. The Fokker-Planck Equation. 2nd ed. New York, NY: Springer-Verlag, 1989. ISBN: 0387504982.
Further Readings
Buy at Amazon Bouchaud, J. P., and M. Potters. Theory of Financial Risks. Cambridge, UK: Cambridge University Press, 2000. ISBN: 0521782325.
Buy at Amazon Crank, J. Mathematics of Diffusion. 2nd ed. Oxford, UK: Clarendon Press, 1975. ISBN: 0198533446.
Buy at Amazon Rudnick, J., and G. Gaspari. Elements of the Random Walk. Cambridge, UK: Cambridge University Press, 2004. ISBN: 0521828910.
Buy at Amazon Spitzer, F. Principles of the Random Walk. 2nd ed. New York, NY: Springer-Verlag, 2001. ISBN: 0387951547.
Stochastic Calculus & Stochastic Process
S.M. Ross, Stochastic Processes, John Wiley & Sons, 1983
A First Course in Stochastic Processes by Samuel Karlin, Howard Taylor
A Second Course in Stochastic Processes by Samuel Karlin, Howard Taylor
The Theory of Stochastic Processes I &II Gikhman, I.I., Skorokhod, A.V
The stochastic processes and applications of Lu Dajin
Of the random process of the Sun
Qian Minping of the theory of stochastic processes, Gong Luguang
Qian Minping, Gong Guanglu, a stochastic process, Peking University Press
Qian Minping, Gong Guanglu, stochastic differential equations, Peking University Press
Probabilistic Methods in Combinatorics
The Probabilistic Method, by N. Alon and J. H. Spencer, 3rd Edition, Wiley, 2008.
Serendipities 