鞅

Topics covered include continuous time Markov chains: birth and death processes and queues, introduction to discrete time martingales, Brownian motion and diffusions.

随机过程简介II：包括：连续时间的马尔可夫链：生灭过程和排队过程，离散时间上的鞅，布朗运动和散射。

Also: the renewal theorem, conditional probability and expectation, regular conditional distributions, stationary sequences aud the bergodic theorem, martingales, and the optimal stopping theorem.

更新理论，条件概率和期望，规则的条件分布，平稳序列和 bergodic 定理，鞅，最优停步理论。泊松过程，布朗运动，强马尔可夫性和不变原则。

Martingales, optimal stopping, Wald's lemma, age-dependent branching processes, stochastic integration, Ito's lemma.

随机过程：随机过程：鞅，最优停步，Wald 引理，依赖年龄的分支过程，随机积分， Ito 引理。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。