Stationary distribution of stochastic population dynamics with infinite delay
type: Item
instance of: scholarly article
title: Stationary distribution of stochastic population dynamics with infinite delay
author: Hao Yang
author: Fuke Wu
author: Peter E. Kloeden
published in: Journal of Differential Equations
publication date: 2022-10-21T00:00:00Z
review text: In this paper, the authors consider the stationary distribution of a stochastic Lotka-Volterra model with infinite delay. The authors use the variable substituting technique to obtain a higher-dimensional stochastic differential equation without delay and then show that the new equation satisfies the strong Feller property and strong Markov property, by which the invariant measure follows from the Krylov-Bogoliubov Theorem. Since distribution of the original model is actually the marginal distribution of the new equation, these results also show that there exists the stationary distribution for the original equation. Furthermore, when the noise intensity is strongly dependent on the population size, the authors also show that the stationary distribution of this stochastic Lotka-Volterra system with infinite delay holds a smooth density by using Hörmander's theorem.
reviewed by: Xuping Zhang
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34K50
zbMATH DE Number: 7604814
zbMATH Keywords: stationary distribution
zbMATH Keywords: stochastic functional differential equation
zbMATH Keywords: infinite delay
zbMATH Keywords: strong Feller property
zbMATH Keywords: Krylov-Bogoliubov theorem
zbMATH Keywords: strong Markov property
MaRDI profile type: Publication
full work available at URL: j.jde.2022.08.035
OpenAlex ID: W4295364742
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DOI: 10.1016/J.JDE.2022.08.035
description: scientific article; zbMATH DE number 7604814