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The Stationary Distribution of Competitive Lotka‐Volterra Population Systems with Jumps

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  • Zhenzhong Zhang
  • Jinying Tong
  • Jianhai Bao

Abstract

Dynamics of Lotka‐Volterra population with jumps (LVWJ) have recently been established (see Bao et al., 2011, and Bao and Yuan, 2012). They provided some useful criteria on the existence of stationary distribution and some asymptotic properties for LVWJ. However, the uniqueness of stationary distribution for n ≥ 2 and asymptotic pathwise estimation limt→+∞⁡(1/t)∫0t |X(s)|pds (p > 0) are still unknown for LVWJ. One of our aims in this paper is to show the uniqueness of stationary distribution and asymptotic pathwise estimation for LVWJ. Moreover, some characterizations for stationary distribution are provided.

Suggested Citation

  • Zhenzhong Zhang & Jinying Tong & Jianhai Bao, 2014. "The Stationary Distribution of Competitive Lotka‐Volterra Population Systems with Jumps," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:820831
    DOI: 10.1155/2014/820831
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    References listed on IDEAS

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    1. 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.
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