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A Two-Step Branching Splitting Model Under Cost Constraint for Rare Event Analysis

Part of: Integral transforms, operational calculus Markov processes

Published online by Cambridge University Press:  14 July 2016

Agnès Lagnoux-Renaudie
Agnès Lagnoux-Renaudie*
Affiliation:
Institut de Mathématique de Toulouse
*
∗Postal address: Institut de Mathématique de Toulouse, Université Paul Sabatier, 31062 Toulouse, France. Email address: lagnoux@cict.fr
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Abstract

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In this paper we consider the splitting method first introduced in rare event analysis. In this technique, the sample paths are split into R multiple copies at various stages to speed up the simulation. Given the cost, the optimization of the algorithm suggests taking all the transition probabilities to be equal; nevertheless, in practice, these quantities are unknown. We address this problem by presenting an algorithm in two phases.

Keywords

Splitting methodsimulation; cost functionLaplace transformGalton–Watson branching processiterated functionrare event

MSC classification

Secondary: 44A10: Laplace transform 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 2 , June 2009 , pp. 429 - 452
Copyright
Copyright © Applied Probability Trust 2009 

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