Quasi-stationary distributions for subcritical branching Markov chains

Fuente: arXiv
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Main Authors: Hong, Wenming, Yao, Dan
Format: Preprint
Published: 2024
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author Hong, Wenming
Yao, Dan
author_facet Hong, Wenming
Yao, Dan
contents Consider a subcritical branching Markov chain. Let $Z_n$ denote the counting measure of particles of generation $n$. Under some conditions, we give a probabilistic proof for the existence of the Yaglom limit of $(Z_n)_{n\in\mathbb{N}}$ by the moment method, based on the spinal decomposition and the many-to-few formula. As a result, we give explicit integral representations of all quasi-stationary distributions of $(Z_n)_{n\in\mathbb{N}}$, whose proofs are direct and probabilistic, and don't rely on Martin boundary theory.
format Preprint
id arxiv_https___arxiv_org_abs_2405_04284
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Quasi-stationary distributions for subcritical branching Markov chains
Hong, Wenming
Yao, Dan
Probability
Consider a subcritical branching Markov chain. Let $Z_n$ denote the counting measure of particles of generation $n$. Under some conditions, we give a probabilistic proof for the existence of the Yaglom limit of $(Z_n)_{n\in\mathbb{N}}$ by the moment method, based on the spinal decomposition and the many-to-few formula. As a result, we give explicit integral representations of all quasi-stationary distributions of $(Z_n)_{n\in\mathbb{N}}$, whose proofs are direct and probabilistic, and don't rely on Martin boundary theory.
title Quasi-stationary distributions for subcritical branching Markov chains
topic Probability
url https://arxiv.org/abs/2405.04284