Local convergence near equilibria for distribution dependent SDEs

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Bibliographic Details
Main Author:	Zhang, Shao-Qin
Format:	Preprint
Published:	2025
Subjects:	Probability 60H10
Online Access:	Acceder al recurso
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author	Zhang, Shao-Qin
author_facet	Zhang, Shao-Qin
contents	Owing to exhibiting phase transitions, we investigate the local convergence near a stationary distribution for distribution dependent stochastic differential equations. By linearizing the nonlinear Markov semigroup associated with the distribution dependent equation around the stationary distribution, the local exponential convergence of the solution is related to the exponential convergence of a semigroup of linear operators. Our result can be used as a criteria for the locally exponential stability of stationary distributions. Concrete examples, including the granular media equation with double-wells landscapes and quadratic interaction, are given to illustrate our main result.
format	Preprint
id	arxiv_https___arxiv_org_abs_2501_04313
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Local convergence near equilibria for distribution dependent SDEs Zhang, Shao-Qin Probability 60H10 Owing to exhibiting phase transitions, we investigate the local convergence near a stationary distribution for distribution dependent stochastic differential equations. By linearizing the nonlinear Markov semigroup associated with the distribution dependent equation around the stationary distribution, the local exponential convergence of the solution is related to the exponential convergence of a semigroup of linear operators. Our result can be used as a criteria for the locally exponential stability of stationary distributions. Concrete examples, including the granular media equation with double-wells landscapes and quadratic interaction, are given to illustrate our main result.
title	Local convergence near equilibria for distribution dependent SDEs
topic	Probability 60H10
url	https://arxiv.org/abs/2501.04313

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