BREAKING A CHAIN OF INTERACTING BROWNIAN PARTICLES

被引：1

作者：

Aurzada, Frank ^{[1
]}

Betz, Volker ^{[1
]}

Lifshits, Mikhail ^{[2
]}

机构：

[1] Tech Univ Darmstadt, Fachbereich Math, Darmstadt, Germany

[2] St Petersburg State Univ, Dept Math & Comp Sci, St Petersburg, Russia

来源：

ANNALS OF APPLIED PROBABILITY | 2021年 / 31卷 / 06期

关键词：

Interacting Brownian particles; stochastic differential equation; Ornstein-Uhlenbeck processes;

D O I：

10.1214/20-AAP1658

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise linear force, with one end of the chain fixed and the other end pulled away at slow speed, in the limit of slow speed and small Brownian noise. We study the instant when the chain "breaks," that is, the distance between two neighbouring particles becomes larger than a certain threshold. There are three different regimes depending on the relation between the speed of pulling and the Brownian noise. We provide weak limit theorems for the break time and the break position for each regime.

引用

页码：2585 / 2611

页数：27

共 33 条

[1] A chain of interacting particles under strain [J].

Allman, Michael ;

Betz, Volker ;

Hairer, Martin .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2011, 121 (09) :2014-2042

[2] Breaking the chain [J].

Allman, Michael ;

Betz, Volker .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2009, 119 (08) :2645-2659

[3]

Aurzada F, 2021, THEOR PROBAB APPL+, V66, P184, DOI [10.1137/S0040585X97T990344, 10.4213/tvp5467]

[4] On Gumbel limit for the length of reactive paths [J].

Bakhtin, Yuri .

STOCHASTICS AND DYNAMICS, 2015, 15 (01)

[5]

Berglund N, 2016, MARKOV PROCESS RELAT, V22, P467

[6] From Random Poincar, Maps to Stochastic Mixed-Mode-Oscillation Patterns [J].

Berglund, Nils ;

Gentz, Barbara ;

Kuehn, Christian .

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2015, 27 (01) :83-136

[7] ON THE NOISE-INDUCED PASSAGE THROUGH AN UNSTABLE PERIODIC ORBIT II: GENERAL CASE [J].

Berglund, Nils ;

Gentz, Barbara .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2014, 46 (01) :310-352

[8] Hunting French ducks in a noisy environment [J].

Berglund, Nils ;

Gentz, Barbara ;

Kuehn, Christian .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (09) :4786-4841

[9]

Berglund Nils, 2006, PROB APPL S

[10]

Bovier A, 2015, GRUNDLEHR MATH WISS, V351, P1, DOI 10.1007/978-3-319-24777-9

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