Second-Order Fast-Slow Stochastic Systems

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-18 DOI:10.1137/23m1567382

Nhu N. Nguyen, George Yin

{"title":"Second-Order Fast-Slow Stochastic Systems","authors":"Nhu N. Nguyen, George Yin","doi":"10.1137/23m1567382","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 5175-5208, August 2024. <br/> Abstract. This paper focuses on systems of nonlinear second-order stochastic differential equations with multiscales. The motivation for our study stems from mathematical physics and statistical mechanics, for example, Langevin dynamics and stochastic acceleration in a random environment. Our aim is to carry out asymptotic analysis to establish large deviations principles. Our focus is on obtaining the desired results for systems under weaker conditions. When the fast-varying process is a diffusion, neither Lipschitz continuity nor linear growth needs to be assumed. Our approach is based on combinations of the intuition from Smoluchowski–Kramers approximation and the methods initiated in [A. A. Puhalskii, Ann. Probab., 44 (2016), pp. 3111–3186] relying on the concepts of relatively large deviations compactness and the identification of rate functions. When the fast-varying process is under a general setup with no specified structure, the paper establishes the large deviations principle of the underlying system under the assumption on the local large deviations principles of the corresponding first-order system.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1567382","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 5175-5208, August 2024.
Abstract. This paper focuses on systems of nonlinear second-order stochastic differential equations with multiscales. The motivation for our study stems from mathematical physics and statistical mechanics, for example, Langevin dynamics and stochastic acceleration in a random environment. Our aim is to carry out asymptotic analysis to establish large deviations principles. Our focus is on obtaining the desired results for systems under weaker conditions. When the fast-varying process is a diffusion, neither Lipschitz continuity nor linear growth needs to be assumed. Our approach is based on combinations of the intuition from Smoluchowski–Kramers approximation and the methods initiated in [A. A. Puhalskii, Ann. Probab., 44 (2016), pp. 3111–3186] relying on the concepts of relatively large deviations compactness and the identification of rate functions. When the fast-varying process is under a general setup with no specified structure, the paper establishes the large deviations principle of the underlying system under the assumption on the local large deviations principles of the corresponding first-order system.

查看原文本刊更多论文

二阶快慢随机系统

SIAM 数学分析期刊》，第 56 卷第 4 期，第 5175-5208 页，2024 年 8 月。摘要本文主要研究多尺度非线性二阶随机微分方程系统。我们的研究动机来自数学物理和统计力学，例如随机环境中的朗格文动力学和随机加速。我们的目的是进行渐近分析，建立大偏差原理。我们的重点是在较弱条件下获得系统的预期结果。当快速变化过程是一个扩散过程时，既不需要假定 Lipschitz 连续性，也不需要假定线性增长。我们的方法基于 Smoluchowskii-Kramers 近似的直觉和 [A. A. Puhalskii, Ann. Probab., 44 (2016), pp.当快变过程处于无特定结构的一般设置下时，本文在假设相应一阶系统的局部大偏差原理的前提下，建立了底层系统的大偏差原理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.