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Exact Sampling of the Infinite Horizon Maximum of a Random Walk Over a Non-linear Boundary

Probability 2016-09-27 v2 Computation

Abstract

We present the first algorithm that samples maxn0{Snnα},\max_{n\geq0}\{S_{n}-n^{\alpha}\}, where SnS_n is a mean zero random walk, and nαn^{\alpha} with α(1/2,1)\alpha\in(1/2,1) defines a nonliner boundary. We show that our algorithm has finite expected running time. We also apply the algorithm to construct the first exact simulation method for the steady-state departure process of a GI/GI/GI/GI/\infty queue where the service time distribution has infinite mean.

Keywords

Cite

@article{arxiv.1609.06402,
  title  = {Exact Sampling of the Infinite Horizon Maximum of a Random Walk Over a Non-linear Boundary},
  author = {Jose Blanchet and Jing Dong and Zhipeng Liu},
  journal= {arXiv preprint arXiv:1609.06402},
  year   = {2016}
}