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Using systematic sampling selection for Monte Carlo solutions of Feynman-Kac equations

Part of: Markov processes Probabilistic methods, simulation and stochastic differential equations Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Ivan Gentil  and
Bruno Rémillard
Ivan Gentil*
Affiliation:
Université Paris-Dauphine
Bruno Rémillard*
Affiliation:
HEC Montréal
*
∗ Postal address: CEREMADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, F-75775 Paris cedex 16, France. Email address: [email protected]
∗∗ Postal address: Service de l'enseignement des méthodes quantitatives de gestion, HEC Montréal, 3000 chemin de la côte-Sainte-Catherine, Montréal, Canada H3T 2A7. Email address: [email protected]
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Abstract

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While the convergence properties of many sampling selection methods can be proven, there is one particular sampling selection method introduced in Baker (1987), closely related to ‘systematic sampling’ in statistics, that has been exclusively treated on an empirical basis. The main motivation of the paper is to start to study formally its convergence properties, since in practice it is by far the fastest selection method available. We will show that convergence results for the systematic sampling selection method are related to properties of peculiar Markov chains.

Keywords

Feynman-Kac formulaesequential Monte Carlogenetic algorithmsystematic samplingMarkov chain

MSC classification

Primary: 65C35: Stochastic particle methods 60G35: Signal detection and filtering
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 2 , June 2008 , pp. 454 - 472
Copyright
Copyright © Applied Probability Trust 2008 

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