| 《随机过程基础》：随机过程理论在数学、科学和工程中有着越来越广泛的应用。《随机过程基础》包括随机过程一些基本而又重要的内容：条件期望，Markov链，Poisson过程和Brown运动：同时也包括Ito积分和随机微分方程等应用范围越来越广的内容。这是一本难得的好书，它1999年出版，到2000年已经是第3次印刷，到2003年则重印到第6次。 |
| 1. review of probability 1.1 events and probability 1.2 random variables 1.3 conditional probability and independence 1.4 solutions 2. conditional expectation 2.1 conditioning on an event 2.2 conditioning on a discrete random variable 2.3 conditioning on an arbitrary random variable 2.4 conditioning on a a-field 2.5 general properties 2.5 various exercises on conditional expectation 2.7 solutions 3 martingales in discrete time 3.1 sequencesofrandomvariables 3.2 filtrations 3.3 martingales 3.4 games or uhance 3.5 stoppingtimes 3.5 optional stopping theorem 3.7 solutions 4 martingale inequalities and convergence 4.1 doob's martingale inequalities …… 5. markov chains 6. stochastic processes in continuous time 7. it5 stochastic calculus index |
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