Random motions at finite speed in higher dimensions
type: Item
instance of: scholarly article
title: Random motions at finite speed in higher dimensions
zbMATH Open document ID: 1155.82017
author: Alexander D. Kolesnik
published in: Journal of Statistical Physics
publication date: 2008-08-20T00:00:00Z
review text: The author investigated the transport process \(X(t),t\geq 0\) in the Euclidean space \(\mathbb{R}^m, m\geq 2\). Based on the analysis of integral transforms of its distributions, the author proved that the joint characteristic function of \(X(t)\) are connected with each other by a convolution-type recurrent relation, and its characteristic function (Fourier transform) satisfies a convolution-type Volterra Integral equation of second kind. In particular, he got the Laplace transform of the characteristic function. Under the standard Kac condition on the speed of the motion and on intensity of the switching Poisson process, he proved the transition density of the isotropic transport process converges to the transition density of the \(m\)-dimensional homogeneous Brownian motion with zero drift and diffusion coefficient depending on the dimension \(m\). Finally he showed that the non-symmertrical random motions can also be treated by similar mothed.
Mathematics Subject Classification ID: 82C70
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 33C10
zbMATH DE Number: 5314329
zbMATH Keywords: random motion
zbMATH Keywords: finite speed transport process
zbMATH Keywords: characteristic function
zbMATH Keywords: Volterra integral equation
reviewed by: Gen Qi Xu
MaRDI profile type: Publication
full work available at URL: s10955-008-9532-0
OpenAlex ID: W2044711402
cites work: Q3671491
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DOI: 10.1007/S10955-008-9532-0
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description: scientific article; zbMATH DE number 5314329