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

Shigeo Kusuoka; Song Liang

doi:10.1080/07362994.2012.668444

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

Shigeo Kusuoka, Song Liang^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	493-528
Number of pages	36
Journal	Stochastic Analysis and Applications
Volume	30
Issue number	3
DOIs	https://doi.org/10.1080/07362994.2012.668444
Publication status	Published - 2012 May
Externally published	Yes

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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10.1080/07362994.2012.668444

Cite this

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

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.",

keywords = "Brownian motion, Classical mechanics, Convergence, Diffusions, Wave field",

author = "Shigeo Kusuoka and Song Liang",

note = "Funding Information: Received June 7, 2011; Accepted June 26, 2011 This work is financially supported by Grant-in-Aid for the Encouragement of Young Scientists (No. 21740063), Japan Society for the Promotion of Science. The authors would like to thank Professor Sergio Albeverio for his careful reading of the manuscript. Address correspondence to Song Liang, Institute of Mathematics, University of Tsukuba, Amakubo 1-1-1, Tsukuba, Ibaraki 305-8571, Japan; E-mail: liang@math.tsukuba.ac.jp",

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doi = "10.1080/07362994.2012.668444",

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AU - Liang, Song

N1 - Funding Information: Received June 7, 2011; Accepted June 26, 2011 This work is financially supported by Grant-in-Aid for the Encouragement of Young Scientists (No. 21740063), Japan Society for the Promotion of Science. The authors would like to thank Professor Sergio Albeverio for his careful reading of the manuscript. Address correspondence to Song Liang, Institute of Mathematics, University of Tsukuba, Amakubo 1-1-1, Tsukuba, Ibaraki 305-8571, Japan; E-mail: liang@math.tsukuba.ac.jp

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N2 - 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.

AB - 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.

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KW - Classical mechanics

KW - Convergence

KW - Diffusions

KW - Wave field

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JO - Stochastic Analysis and Applications

JF - Stochastic Analysis and Applications

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

Abstract

Keywords

ASJC Scopus subject areas

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