阅读材料:

Gabor J. Szekely and Donald St. P. Richards, The St. Petersburg Paradox and the Crash of High-Tech Stocks in 2000

F.T. Leighton,R.L. Rivest, Estimating a Probability Using Finite Memory, IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. IT-32, NO. 6, 1986, 733--742.

Joseph T. Chang, Markov Chains, Course notes, 2001.

Chad Casarotto, Markov chains and the ergodic theorem, University of Chicago VIGRE REU thesis, 2007.

语录:

"This algorithm has been proved to work, but has never been observed to do so" (about the Monte Carlo Markov Chain method for approximate counting of contingency tables). Alexander Barvinok (Joint Summer Research Conference, Snowbird, UT, 7/16/03, Illinois Mathematics Colloquium, 02/05, and Joint Summer Research Conference, Snowbird, UT, 6/15/06)

Probability is a mathematical discipline whose aims are akins to those, for example, of geometry of analytical mechanics. In each field we must carefully distinguish three aspects of the theory: (a) the formal logical content, (b) the intuitive background, and (c) the applications. The character, and the charm, of the whole structure cannot be appreciated without considering all three aspects in their proper relation. -- William Feller, An Introduction to Probability Theory and its Applications

课本勘误: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

习题解答:

杨默涵, 黄桑霞, 毕竞烨, 林东12, 李子汨, 朱一和,1,2, 潘俊峰, 陈相如

潘俊峰,林庆樑,An exercise on total variation estimate

徐冠中, 吴天翔,An exercise on total variation estimate

潘俊峰,林庆樑,An exercise on total variation estimate

徐冠中, 林东,Markov Chain

林东, 徐冠中, Markov Chain

潘俊峰, 欧阳希修,Markov Chain

其它:

何律恒, A bijection between planted plane trees and Dyck words

朱一和, 随机徘徊主引理

徐冠中, 1, 2

林冰凯, 一个大偏差估计

汤龑鸣, Kolmogorov方程

陈相如, Bernstein多项式

施江虹, Ergodic Theorem

郭奇, 陈天奇, 本原马氏链

陈天奇, 独立同分布的随机变量强大数定律的证明整理, Coupon Collector, Ergodic Theorem, A Coin Flipping Problem

欧阳希修, 优惠券问题

李亮达, 耦合方法, 常返的判定, 弱强大数定律和中心极限定理, 关于MCMC与耦合的一点补充

陆晔琦, 概率极限定理整理

吴东宏, MC状态分类

杜霖, Hidden Markov Models

任腾, Hidden Markov Models, MCMC算法与硬核模型

毕竞烨, 齐次Markov Chain的计算机模拟, 齐次Markov Chain的大数定律

黄桑霞, 陈相如, 马尔可夫链在计数问题中的一个应用

吴天翔,袁若石 常见概率分布

孙辛若,林东 圣彼得堡悖论

赵一振

2007年12月28日10点-11点50,下院108,期末考试