Journal of Applied Probability

Conditions for permanence and ergodicity of certain stochastic predator-prey models

Nguyen Huu Du, Dang Hai Nguyen, and G. George Yin

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Abstract

In this paper we derive sufficient conditions for the permanence and ergodicity of a stochastic predator-prey model with a Beddington-DeAngelis functional response. The conditions obtained are in fact very close to the necessary conditions. Both nondegenerate and degenerate diffusions are considered. One of the distinctive features of our results is that they enable the characterization of the support of a unique invariant probability measure. It proves the convergence in total variation norm of the transition probability to the invariant measure. Comparisons to the existing literature and matters related to other stochastic predator-prey models are also given.

Article information

Source
J. Appl. Probab. Volume 53, Number 1 (2016), 187-202.

Dates
First available in Project Euclid: 8 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.jap/1457470568

Mathematical Reviews number (MathSciNet)
MR3471956

Zentralblatt MATH identifier
1338.34091

Subjects
Primary: 34C12: Monotone systems 60H10: Stochastic ordinary differential equations [See also 34F05] 92D25: Population dynamics (general)

Keywords
Ergodicity extinction permanence predator-prey Beddington-DeAngelis functional response stationary distribution

Citation

Du, Nguyen Huu; Nguyen, Dang Hai; Yin, G. George. Conditions for permanence and ergodicity of certain stochastic predator-prey models. J. Appl. Probab. 53 (2016), no. 1, 187--202. https://projecteuclid.org/euclid.jap/1457470568.


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