Subsolutions of an Isaacs Equation and Efficient Schemes for Importance Sampling
Subsolutions of an Isaacs Equation and Efficient Schemes for Importance Sampling
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DOI：
10.1287/moor.1070.0266
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发表时间：
2005-08
期刊：
影响因子：
--
通讯作者：
P. Dupuis;Hui Wang
中科院分区：
文献类型：
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作者：
P. Dupuis;Hui Wang
摘要：作者以前的论文建立了估计罕见事件概率的重要性抽样算法之间的联系，两人零和微分游戏，以及相关的艾萨克斯方程。为了在一般情况下构造近似最优方案，必须考虑动态方案，即，在单个模拟过程中，可以取决于直到那时的模拟结果的测量变化。本文及其配套文件表明，经典意义下的Isaacs方程的解提供了一个基本的和灵活的工具，建设和分析的近最优方案。渐近分析是本论文的主题，而配套文件的重点是明确的方法，子解的建设，实施方面和数值结果。
Abstract : Previous papers by authors establish the connection between importance sampling algorithms for estimating rare-event probabilities, two-person zero-sum differential games, and the associated Isaacs equation. In order to construct nearly optimal schemes in a general setting, one must consider dynamic schemes, i.e., changes of measure that, in the course of a single simulation, can depend on the outcome of the simulation up till that time. The present paper and a companion paper show that classical sense subsolutions of the Isaacs equation provide a basic and flexible tool for the construction and analysis of nearly optimal schemes. Asymptotic analysis is the topic of the present paper, while the companion paper focuses on explicit methods for the construction of subsolutions, implementation aspects and numerical results.