Path-ZVA Simulation Method for Time-Bounded Rare Events in a Semi-Markov Chain

Daniël  Reijsbergen; Pieter-Tjerk de Boer; Werner R.W. Scheinhardt

Path-ZVA Simulation Method for Time-Bounded Rare Events in a Semi-Markov Chain

Daniël Reijsbergen^*, Pieter-Tjerk de Boer, Werner R.W. Scheinhardt

^*Corresponding author for this work

Research output: Contribution to conference › Abstract › Academic

Abstract

We present an importance-sampling simulation method for estimating the probability of a time-bounded rare event in a Semi-Markov chain. Our method is based on generalizing the Path-ZVA method developed earlier for Markov chains, which works by first finding which paths are asymptotically dominant, and then using them to approximate the theoretical zero-variance change of measure. Our method requires only mild assumptions about the tails of the chain's sojourn time distributions. We present an empirical study that shows that our method has desirable efficiency properties in this setting.

Original language	English
Publication status	Published - 2021
Event	13th International Workshop on Rare-Event Simulation, RESIM 2021 - online, Paris, France Duration: 18 May 2021 → 21 May 2021 Conference number: 13 https://resim2021.sciencesconf.org/

Workshop

Workshop	13th International Workshop on Rare-Event Simulation, RESIM 2021
Abbreviated title	RESIM 2021
Country/Territory	France
City	Paris
Period	18/05/21 → 21/05/21
Internet address	https://resim2021.sciencesconf.org/

Cite this

@conference{a60e695b77a2444a9e865700536a618f,

title = "Path-ZVA Simulation Method for Time-Bounded Rare Events in a Semi-Markov Chain",

abstract = "We present an importance-sampling simulation method for estimating the probability of a time-bounded rare event in a Semi-Markov chain. Our method is based on generalizing the Path-ZVA method developed earlier for Markov chains, which works by first finding which paths are asymptotically dominant, and then using them to approximate the theoretical zero-variance change of measure. Our method requires only mild assumptions about the tails of the chain's sojourn time distributions. We present an empirical study that shows that our method has desirable efficiency properties in this setting.",

author = "Dani{\"e}l Reijsbergen and {de Boer}, Pieter-Tjerk and Scheinhardt, {Werner R.W.}",

year = "2021",

language = "English",

note = "13th International Workshop on Rare-Event Simulation, RESIM 2021 , RESIM 2021 ; Conference date: 18-05-2021 Through 21-05-2021",

url = "https://resim2021.sciencesconf.org/",

}

TY - CONF

T1 - Path-ZVA Simulation Method for Time-Bounded Rare Events in a Semi-Markov Chain

AU - Reijsbergen, Daniël

AU - de Boer, Pieter-Tjerk

AU - Scheinhardt, Werner R.W.

N1 - Conference code: 13

PY - 2021

Y1 - 2021

N2 - We present an importance-sampling simulation method for estimating the probability of a time-bounded rare event in a Semi-Markov chain. Our method is based on generalizing the Path-ZVA method developed earlier for Markov chains, which works by first finding which paths are asymptotically dominant, and then using them to approximate the theoretical zero-variance change of measure. Our method requires only mild assumptions about the tails of the chain's sojourn time distributions. We present an empirical study that shows that our method has desirable efficiency properties in this setting.

AB - We present an importance-sampling simulation method for estimating the probability of a time-bounded rare event in a Semi-Markov chain. Our method is based on generalizing the Path-ZVA method developed earlier for Markov chains, which works by first finding which paths are asymptotically dominant, and then using them to approximate the theoretical zero-variance change of measure. Our method requires only mild assumptions about the tails of the chain's sojourn time distributions. We present an empirical study that shows that our method has desirable efficiency properties in this setting.

M3 - Abstract

T2 - 13th International Workshop on Rare-Event Simulation, RESIM 2021

Y2 - 18 May 2021 through 21 May 2021

ER -

Path-ZVA Simulation Method for Time-Bounded Rare Events in a Semi-Markov Chain

Abstract

Workshop

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