The particle approximation of quasi-stationary distributions. Part~I: concentration bounds in the uniform case

Fuente: arXiv
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Autori principali: Journel, Lucas, Rousset, Mathias
Natura: Preprint
Pubblicazione: 2024
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author Journel, Lucas
Rousset, Mathias
author_facet Journel, Lucas
Rousset, Mathias
contents We study mean-field particle approximations of normalized Feynman-Kac semi-groups, usually called Fleming-Viot or Feynman-Kac particle systems. Assuming various large time stability properties of the semi-group uniformly in the initial condition, we provide explicit time-uniform $L^p$ and exponential bounds (a new result) with the expected rate in terms of sample size. This work is based on a stochastic backward error analysis (similar to the classical concept of numerical analysis) of the measure-valued Markov particle estimator, an approach that simplifies methods previously used for time-uniform $L^p$ estimates.
format Preprint
id arxiv_https___arxiv_org_abs_2412_15820
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The particle approximation of quasi-stationary distributions. Part~I: concentration bounds in the uniform case
Journel, Lucas
Rousset, Mathias
Probability
We study mean-field particle approximations of normalized Feynman-Kac semi-groups, usually called Fleming-Viot or Feynman-Kac particle systems. Assuming various large time stability properties of the semi-group uniformly in the initial condition, we provide explicit time-uniform $L^p$ and exponential bounds (a new result) with the expected rate in terms of sample size. This work is based on a stochastic backward error analysis (similar to the classical concept of numerical analysis) of the measure-valued Markov particle estimator, an approach that simplifies methods previously used for time-uniform $L^p$ estimates.
title The particle approximation of quasi-stationary distributions. Part~I: concentration bounds in the uniform case
topic Probability
url https://arxiv.org/abs/2412.15820