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Phase transitions of some non-linear stochastic models

Part of: Markov processes Equilibrium statistical mechanics

Published online by Cambridge University Press:  14 July 2016

Shui Feng
Shui Feng*
Affiliation:
McMaster University
*
∗Postal address: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L85 4K1.
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Abstract

A class of non-linear stochastic models is introduced. Phase transitions, critical points and the domain of attraction are discussed in detail for some concrete examples. For one of the examples the explicit expression for the domain of attraction and the rates of convergence are obtained.

Keywords

STATIONARY DISTRIBUTIONCRITICAL POINTDOMAIN OF ATTRACTIONLINEAR STABILITY ANALYSIS

MSC classification

Primary: 60J75: Jump processes
Secondary: 82B26: Phase transitions (general) 82B27: Critical phenomena
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 1 , March 1995 , pp. 193 - 201
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Supported by the SERB grant of McMaster University.

References

[1] Boyce, W. E. and Diprima, R. C. (1986) Elementary Differential Equations, 4th edn. Wiley, New York.Google Scholar
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[3] Dawson, D. A. (1983) Critical dynamics and fluctuations for a mean-field model of cooperative behavior. J. Statist. Phys. 31, 29–85.CrossRefGoogle Scholar
[4] Feng, S. and Zheng, X. (1992) Solutions of a class of nonlinear master equations. Stoch. Proc. Appl. 43, 65–84.Google Scholar