Array-RQMC to Speed up the Simulation for Estimating the Hitting-Time Distribution to a Rare Set of a Regenerative System

Document Type

Syllabus

Publication Date

1-1-2022

Abstract

Estimating the distribution of the hitting time to a rarely visited set of states presents substantial challenges. We recently designed simulation-based esti­mators to exploit existing theory for regenerative systems that a scaled geometric sum of independent and identically distributed random variables weakly converges to an exponential random variable as the geometric’s parameter vanishes. The result­ing approximation then reduces the estimation of the distribution to estimating just the mean of the limiting exponential variable. The present work examines how ran­domized quasi-Monte Carlo (RQMC) techniques can help to reduce the variance of the estimators. Estimating hitting-time properties entails simulating a stochastic (here Markov) process, for which the so-called array-RQMC method is suited. After describing its application, we illustrate numerically the gain on a standard rare-event problem. This chapter combines ideas from several areas in which Pierre L’Ecuyer has made fundamental theoretical and methodological contributions: randomized quasi-Monte Carlo methods, rare-event simulation, and distribution estimation.

Identifier

85162666988 (Scopus)

ISBN

[9783031101922, 9783031101939]

Publication Title

Advances in Modeling and Simulation Festschrift for Pierre L Ecuyer

External Full Text Location

https://doi.org/10.1007/978-3-031-10193-9_17

First Page

333

Last Page

351

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