The stationary distribution of the facultative population model with a degenerate noise

In this paper, we consider the stationary distribution of the facultative population model with a degenerate noise. The contributions of this paper lie in: (a) providing sufficient conditions which allow the noise intensity matrix to be degenerate, and, in particular, guarantee the existence and uni...

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Bibliographic Details
Published in:Statistics & probability letters 2013-02, Vol.83 (2), p.655-664
Main Authors: Tong, Jinying, Zhang, Zhenzhong, Bao, Jianhai
Format: Article
Language:English
Subjects:
Feller property
Lotka–Volterra model
Rate of convergence
Stationary distribution
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Summary:In this paper, we consider the stationary distribution of the facultative population model with a degenerate noise. The contributions of this paper lie in: (a) providing sufficient conditions which allow the noise intensity matrix to be degenerate, and, in particular, guarantee the existence and uniqueness of the stationary distribution of our model; (b) discussing the property of positive recurrence of the model and revealing that the associated transition probability function converges exponentially to the unique stationary distribution; (c) showing the integral equation that the Laplace transform of the stationary distribution satisfies.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2012.11.003