To the top

Page Manager: Webmaster
Last update: 9/11/2012 3:13 PM

Tell a friend about this page
Print version

The Kac master equation w… - University of Gothenburg, Sweden Till startsida
Sitemap
To content Read more about how we use cookies on gu.se

The Kac master equation with unbounded collision rate

Journal article
Authors Bernt Wennberg
Mattias Sundén
Published in Markov Processes and Related Fields
Volume 15
Issue 2
Pages 125-148
ISSN 1024-2953
Publication year 2009
Published at Department of Mathematical Sciences, Mathematical Statistics
Department of Mathematical Sciences, Mathematics
Pages 125-148
Language en
Keywords Brownian motion, collision kernel, Feller processes, innitesimal generator, Kac model, Laplace - Beltrami operator, Markov process, semigroup, spectral gap
Subject categories Mathematical Analysis, Mathematical statistics, Other Mathematics

Abstract

The Kac model is a Markov jump process on the sphere $\sum_{j=1}^{N} v_j^2$. The model was conceived as model for an N-particle system with pairwise interactions, and hence the jumps involve only pairs of coordinates, $(v_i, v_j )$. This paper deals with Kac models with unbounded jump rates. We prove that the processes are Feller processes, and introduce a diusion approximation that is useful for numerical simulation of the processes. We also study the spectral gap of the Markov generators, using the methods developed by Carlen, Carvalho and Loss.

Page Manager: Webmaster|Last update: 9/11/2012
Share:

The University of Gothenburg uses cookies to provide you with the best possible user experience. By continuing on this website, you approve of our use of cookies.  What are cookies?