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A stochastic competing-species model and ergodicity

Part of: Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Zengjing Chen  and
Reg Kulperger
Zengjing Chen*
Affiliation:
Shandong University
Reg Kulperger*
Affiliation:
The University of Western Ontario
*
∗Postal address: Department of Mathematics, Shandong University, Jinan, 250100, P. R. China.
∗∗Postal address: Department of Statistical and Actuarial Science, The University of Western Ontario, London, Ontario N6A 5B7, Canada. Email address: [email protected]
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Abstract

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We consider a classic competing-species model with the rates changed to include Gaussian white noise. We show that if the noise is not too large, then the stochastic version is ergodic. An explicit relation between the noise and the original competing-species parameters gives a sufficient condition for ergodicity.

Keywords

Competing speciesstochasticItô processBrownian motionergodic

MSC classification

Primary: 60H10: Stochastic ordinary differential equations
Secondary: 60G99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 738 - 753
Copyright
© Applied Probability Trust 2005 

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