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Long Term Behaviour of Locally Interacting Birth-and-Death Processes

Shcherbakov, Vadim and Volkov, Stanislav LU (2015) In Journal of Statistical Physics 158(1). p.132-157
Abstract
In this paper we study long-term evolution of a finite system of locally interacting birth-and-death processes labelled by vertices of a finite connected graph. A detailed description of the asymptotic behaviour is obtained in the case of both constant vertex degree graphs and star graphs. The model is motivated by modelling interactions between populations, adsorption-desorption processes and is related to interacting particle systems, Gibbs models with unbounded spins, as well as urn models with interaction.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Markov chain, Birth-and-death process, Gibbs measure, Reversibility, Recurrence, Transience, Explosion
in
Journal of Statistical Physics
volume
158
issue
1
pages
132 - 157
publisher
Springer
external identifiers
  • wos:000347874500007
  • scopus:84921938925
ISSN
1572-9613
DOI
10.1007/s10955-014-1122-8
language
English
LU publication?
yes
id
3c612753-85e9-44d0-99b3-ae9a6fcaf3c9 (old id 5070033)
date added to LUP
2015-02-25 15:38:33
date last changed
2017-03-15 11:31:24
@article{3c612753-85e9-44d0-99b3-ae9a6fcaf3c9,
  abstract     = {In this paper we study long-term evolution of a finite system of locally interacting birth-and-death processes labelled by vertices of a finite connected graph. A detailed description of the asymptotic behaviour is obtained in the case of both constant vertex degree graphs and star graphs. The model is motivated by modelling interactions between populations, adsorption-desorption processes and is related to interacting particle systems, Gibbs models with unbounded spins, as well as urn models with interaction.},
  author       = {Shcherbakov, Vadim and Volkov, Stanislav},
  issn         = {1572-9613},
  keyword      = {Markov chain,Birth-and-death process,Gibbs measure,Reversibility,Recurrence,Transience,Explosion},
  language     = {eng},
  number       = {1},
  pages        = {132--157},
  publisher    = {Springer},
  series       = {Journal of Statistical Physics},
  title        = {Long Term Behaviour of Locally Interacting Birth-and-Death Processes},
  url          = {http://dx.doi.org/10.1007/s10955-014-1122-8},
  volume       = {158},
  year         = {2015},
}