Blanchet J, Dong J, Liu Z. Exact sampling of the infinite horizon maximum of a random walk over a nonlinear boundary. Journal of Applied Probability. 2019;56(1):116-138. doi:10.1017/jpr.2019.9
Abstract
We present the first algorithm that samples maxn≥0{Sn − nα}, where Sn is a mean zero random walk, and nα with defines a nonlinear boundary. We show that our algorithm has finite expected running time. We also apply this algorithm to construct the first exact simulation method for the steady-state departure process of a GI/GI/∞ queue where the service time distribution has infinite mean.
Authors
Jose Blanchet, Jing Dong, Zhipeng Liu
Publication date
2019/3
Journal
Journal of Applied Probability
Volume
56
Issue
1
Pages
116-138
Publisher
Cambridge University Press
