Hostname: page-component-5cf477f64f-bmd9x Total loading time: 0 Render date: 2025-04-05T02:12:57.849Z Has data issue: false hasContentIssue false
  • English
  • Français

On transient behaviour of a nearest-neighbour birth-death process on a lattice

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Boris L. Granovsky  and
Liat Rozov
Boris L. Granovsky
Affiliation:
Technion — Israel Institute of Technology
Liat Rozov*
Affiliation:
Technion — Israel Institute of Technology
*
∗ Postal address for both authors: Department of Mathematics, Technion, Haifa, 32000, Israel.
Get access Rights & Permissions [Opens in a new window]

Abstract

We provide the explicit expression for the mean coverage function of a generalized voter model on a regular lattice and establish a characterization of the class of the above processes. As a result, we derive the exact rate of convergence of the considered processes to the steady state. We also prove the existence of different processes with the same mean coverage function on a given lattice.

Keywords

NEAREST-NEIGHBOUR INTERACTING PARTICLE SYSTEMSMEAN COVERAGE FUNCTIONRATE OF EXPONENTIONAL CONVERGENCE

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60K25: Queueing theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 31 , Issue 2 , June 1994 , pp. 549 - 553
Copyright
Copyright © Applied Probability Trust 1994 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Financial support from the Fund for the Promotion of Research at Technion to the first author is gratefully acknowledged.

References

Belitsky, V. and Granovsky, B. L. (1991) On the dynamics of the stochastic model of adsorption-desorption on a finite lattice. Commun. Statist. - Stoch. Models 7, 327–341.Google Scholar
Belitsky, V. and Granovsky, B. L. (1992) Nearest neighbor spin systems: Time dynamics of the mean coverage density function and inference on parameters. Preprint.Google Scholar
Durrett, R. (1988) Lecture Notes on Particle Systems and Percolation. Wadsworth & Brooks/Cole, San Francisco, CA.Google Scholar
Granovsky, B. L., Rolski, T. Woyczynski, W. A. and Mann, J. A. (1989) A general stochastic model of adsorption-desorption: transient behavior. Chemometrics and Intelligent Laboratory Systems 6, 273–280.CrossRefGoogle Scholar
Liggett, T. M. (1985) Interacting Particle Systems. Springer-Verlag, New York.CrossRefGoogle Scholar
Ycart, B., Woyczynski, W. A., Szulga, J., Reazor, S. and Mann, J. A. (1989) An interacting particle model of adsorption. Appl. Math. 20, 3.Google Scholar