Blind Simulation and Regenerative Processes

摘要：NCR-9505443，威斯康星大学麦迪逊分校，盲模拟和再生过程，PI-James A。Bucklew和Peter E. Ney：重要性抽样用于加速稀有事件的蒙特卡罗模拟。 到目前为止所使用的方法需要精确的知识的基本概率结构的系统被模拟。 直接蒙特卡罗模拟只需要一个遍历性的假设，以保证系统参数的相对频率估计将收敛到真值。 直接蒙特卡罗技术是盲模拟技术的一个例子：这是一种通用的方法，在没有确切的潜在概率定律知识的情况下自举。 迄今为止取得的一些部分结果表明，在许多有趣的情况下，盲技术可以执行以及那些利用更多的先验信息。 应用于记忆系统（例如马尔可夫），这些技术自然会导致再生过程的研究。 这些过程在随机的时间停止，基本上又重新开始。 这些过程的理论方面还有待发展，需要盲目的模拟方法的分析。 盲模拟和再生过程的研究在系统模拟器可用的技巧中非常重要。** 奥布里M.布什计划主任，代理副主任网络和通信研究和结构部国家科学基金会

ABSTRACT: NCR-9505443, University of Wisconsin-Madison, Blind Simulation and Regenerative Processes, PI-James A. Bucklew and Peter E. Ney: Importance sampling is used to speed up Monte Carlo simulation of rare events. The methods used to date have required exact knowledge of the underlying probability structure of the system being simulated. Direct Monte Carlo simulation requires only an assumption of ergodicity to guarantee that relative frequency estimates of system parameters will converge to true values. The direct Monte Carlo technique is an example of a blind simulation technique: a generic class of methodologies which bootstrap their way without exact knowledge of the underlying probability law. Some partial results achieved to date indicate that in many interesting situations, blind techniques can perform just about as well as those utilizing much more prior information. Applied to systems with memory (Markovian for example) these techniques lead naturally to the study of regenerative processes. These are processes that at random times stop and essentially start themselves over again. Aspects of the theory of these processes are yet to be developed and are needed for the analysis of blind simulation methods. This study of blind simulation and regenerative processes promises to very important in the bag of tricks available to system simulators.***************************************************************************** Aubrey M. BushProgram Director, Acting Deputy Divison DirectorDivision of Networking and Communica tions Research and InfrastructureNational Science Foundation