{"title":"Wasserstein convergence rate of invariant measures for stochastic Schrödinger delay lattice systems","authors":"Zhang Chen , Dandan Yang , Shitao Zhong","doi":"10.1016/j.jde.2024.08.065","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is concerned with the convergence of invariant measures in the Wasserstein sense for the stochastic Schrödinger delay lattice systems as delay parameter <em>ρ</em> or parameter <em>β</em> approaches zero. Through <em>p</em>th-order moment estimates of solutions to systems, as well as the Hölder continuity estimates of solutions with respect to time, we obtain the convergence of solutions about initial data and the above parameters. Then together with high-order moment estimates of invariant measures, we prove that the unique invariant measure of such delay lattice system converges to the invariant measure of limiting system in the Wasserstein sense as delay parameter <em>ρ</em> or parameter <em>β</em> approaches zero, and the corresponding convergence rate is also obtained.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039624005540","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is concerned with the convergence of invariant measures in the Wasserstein sense for the stochastic Schrödinger delay lattice systems as delay parameter ρ or parameter β approaches zero. Through pth-order moment estimates of solutions to systems, as well as the Hölder continuity estimates of solutions with respect to time, we obtain the convergence of solutions about initial data and the above parameters. Then together with high-order moment estimates of invariant measures, we prove that the unique invariant measure of such delay lattice system converges to the invariant measure of limiting system in the Wasserstein sense as delay parameter ρ or parameter β approaches zero, and the corresponding convergence rate is also obtained.
期刊介绍:
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics