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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

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.

Suggested Citation

  • Tong, Jinying & Zhang, Zhenzhong & Bao, Jianhai, 2013. "The stationary distribution of the facultative population model with a degenerate noise," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 655-664.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:655-664
    DOI: 10.1016/j.spl.2012.11.003
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    References listed on IDEAS

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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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    3. Zhang, Zhenzhong & Zhang, Xuekang & Tong, Jinying, 2017. "Exponential ergodicity for population dynamics driven by α-stable processes," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 149-159.
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    6. Zhao, Dianli & Yuan, Sanling, 2018. "Sharp conditions for the existence of a stationary distribution in one classical stochastic chemostat," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 199-205.

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