A Mechanical Model of Brownian Motion for One Massive Particle Including Slow Light Particles

2017 ◽  
Vol 170 (2) ◽  
pp. 286-350
Author(s):  
Song Liang
Keyword(s):  
Brownian Motion ◽  
Mechanical Model ◽  
Slow Light ◽  
Massive Particle ◽  
Light Particles

A mechanical model of Brownian motion for one massive particle including low energy light particles in dimension d ≥ 3

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Song Liang
Keyword(s):  
Brownian Motion ◽  
Mechanical Model ◽  
Slow Light ◽  
Massive Particle ◽  
Ideal Gas ◽  
Low Energy ◽  
High Dimensional ◽  
Stat Phys ◽  
High Dimensional Case ◽  
Light Particles

Abstract We provide a connection between Brownian motion and a classical Newton mechanical system in dimension d ≥ 3 {d\geq 3} . This paper is an extension of [S. Liang, A mechanical model of Brownian motion for one massive particle including slow light particles, J. Stat. Phys. 170 2018, 2, 286–350]. Precisely, we consider a system of one massive particle interacting with an ideal gas, evolved according to non-random Newton mechanical principles, via interaction potentials, without any assumption requiring that the initial energies of the environmental particles should be restricted to be “high enough”. We prove that, as in the high-dimensional case, the position/velocity process of the massive particle converges to a diffusion process when the mass of the environmental particles converges to 0, while the density and the velocities of them go to infinity.

A mechanical model for the Brownian motion of a convex body

1983 ◽  
Vol 62 (4) ◽  
pp. 427-448 ◽  
Author(s):  
D. D�rr ◽  
S. Goldstein ◽  
J. L. Lebowitz
Keyword(s):  
Brownian Motion ◽  
Convex Body ◽  
Mechanical Model

scholarly journals A mechanical model of Brownian motion

1981 ◽  
Vol 78 (4) ◽  
pp. 507-530 ◽  
Author(s):  
D. Dürr ◽  
S. Goldstein ◽  
J. L. Lebowitz
Keyword(s):  
Brownian Motion ◽  
Mechanical Model

A CLASSICAL MECHANICAL MODEL OF BROWNIAN MOTION WITH PLURAL PARTICLES

2010 ◽  
Vol 22 (07) ◽  
pp. 733-838 ◽  
Author(s):  
SHIGEO KUSUOKA ◽  
SONG LIANG
Keyword(s):  
Brownian Motion ◽  
Diffusion Process ◽  
Mechanical Model ◽  
Existence And Uniqueness ◽  
Diffusion Processes ◽  
Scaling Limit ◽  
Mechanical Systems ◽  
Ideal Gas ◽  
Uniqueness Of The Solution ◽  
Precise Expression

We give a connection between diffusion processes and classical mechanical systems in this paper. Precisely, we consider a system of plural massive particles interacting with an ideal gas, evolved according to classical mechanical principles, via interaction potentials. 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.

A mechanical model of Brownian motion in half-space

1989 ◽  
Vol 55 (3-4) ◽  
pp. 649-693 ◽  
Author(s):  
Paola Calderoni ◽  
Detlef D�rr ◽  
Shigeo Kusuoka
Keyword(s):  
Brownian Motion ◽  
Half Space ◽  
Mechanical Model

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

Brownian motion with quadratic killing and some implications

1986 ◽  
Vol 23 (04) ◽  
pp. 893-903 ◽  
Author(s):  
Michael L. Wenocur
Keyword(s):  
Brownian Motion ◽  
Weibull Distribution ◽  
Special Function ◽  
Function Theory ◽  
Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

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