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

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  • Tong, Jinying
  • Zhang, Zhenzhong
  • Bao, Jianhai
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    Abstract

    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212004105
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 2 ()
    Pages: 655-664

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:655-664

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    Related research

    Keywords: Lotka–Volterra model; Stationary distribution; Feller property; Rate of convergence;

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    1. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
    2. Yuan, Chenggui & Mao, Xuerong, 2003. "Asymptotic stability in distribution of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 277-291, February.
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