随机模拟中减小方差的似然比法

引进似然比过程把一种分布下的期望用另一种分布的期望代替。似然比过程的鞅性质允许其把区间末端的值通过取条件期望用区间中间的值代替，在满足一定条件下，达到减小方差。反Ｇｌａｓｓｅｒｍａｎ讨论末端为固定正整数的情形推广到末端是取正整数的随机变量的情形，同时应用到排队模型中单个服务台的成批到达的顾客等待时间的方差减小的问题。

Variance Reduction of Stochastic Simulation: Likelihood Ratio Method

Likelihood ratio is used to estimate an expectation under one distribution from the expection of another distribution.By taking a conditional expectation,the likelihood ratio can replace its value at the end of an interval with values at intermediate times,due to its martingale property.Hence,under some conditions,the variance can be reduced.The case that the end of an interval was a fixed non negative integer,given by Glasserman,is extended to some random variables that take non negative integer values.Finally,this method is used to solve the waiting time problem of bulk arrival queues.