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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 820831, 7 pages
http://dx.doi.org/10.1155/2014/820831
Research Article

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

1College of Science, Donghua University, Shanghai 201620, China
2Department of Mathematics, Central South University, Changsha 410075, China

Received 17 December 2013; Accepted 16 January 2014; Published 13 March 2014

Academic Editor: Litan Yan

Copyright © 2014 Zhenzhong Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 and asymptotic pathwise estimation 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.