## Abstract and Applied Analysis

### The Stationary Distribution of Competitive Lotka-Volterra Population Systems with Jumps

#### 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 $n\ge \mathrm{2}$ and asymptotic pathwise estimation ${\mathrm{lim}}_{t\to +\mathrm{\infty }}(1/\mathrm{t)}{\int }_{\mathrm{0}}^{t}\mathrm{‍}|X(s){|}^{p}d\mathrm{s }$ $(p>\mathrm{0})$ 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 820831, 7 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412606756

Digital Object Identifier
doi:10.1155/2014/820831

Mathematical Reviews number (MathSciNet)
MR3182305

Zentralblatt MATH identifier
07023144

#### Citation

Zhang, Zhenzhong; Tong, Jinying; Bao, Jianhai. The Stationary Distribution of Competitive Lotka-Volterra Population Systems with Jumps. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 820831, 7 pages. doi:10.1155/2014/820831. https://projecteuclid.org/euclid.aaa/1412606756

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