A Classical Mechanical Model of Brownian Motion with One Particle Coupled to a Random Wave Field

Shigeo Kusuoka, Song Liang

Research output: Contribution to journalArticle

Abstract

We consider the problem of deriving Brownian motions from classical mechanical systems. Specifically, we consider a system with one massive particle coupling to an ideal random wave field, evolved according to classical mechanical principles. We prove the almost sure existence and uniqueness of the solution of the considered dynamics, prove the convergence of the solution under a certain scaling limit and give the precise expression of the limiting process, a diffusion process.

Original languageEnglish
Pages (from-to)493-528
Number of pages36
JournalStochastic Analysis and Applications
Volume30
Issue number3
DOIs
Publication statusPublished - 2012 May
Externally publishedYes

Keywords

  • Brownian motion
  • Classical mechanics
  • Convergence
  • Diffusions
  • Wave field

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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