STEADY-STATE SIMULATION OF REFLECTED BROWNIAN MOTION AND RELATED STOCHASTIC NETWORKS

• 成果类型: Article
• 署名作者: Blanchet, Jose; Chen, Xinyun
• 署名单位: Columbia University; State University of New York (SUNY) System; Stony Brook University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1072
• 发表日期: 2015
• 页码: 3209-3250
• 关键词: exit times; approximations; STABILITY

摘要

This paper develops the first class of algorithms that enable unbiased estimation of steady-state expectations for multidimensional reflected Brownian motion. In order to explain our ideas, we first consider the case of compound Poisson (possibly Markov modulated) input. In this case, we analyze the complexity of our procedure as the dimension of the network increases and show that, under certain assumptions, the algorithm has polynomial-expected termination time. Our methodology includes procedures that are of interest beyond steady-state simulation and reflected processes. For instance, we use wavelets to construct a piecewise linear function that can be guaranteed to be within 8 distance (deterministic) in the uniform norm to Brownian motion in any compact time interval.