Open Access Research

Pathwise estimation of stochastic functional Kolmogorov-type systems with infinite delay

Enwen Zhu1 and Yong Xu2*

Author Affiliations

1 School of Mathematics and Computing Sciences, Changsha University of Science and Technology, Changsha, Hunan, 410076, China

2 School of Mathematics, Central South University, Changsha, Hunan, 410075, China

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Journal of Inequalities and Applications 2012, 2012:171 doi:10.1186/1029-242X-2012-171

Published: 1 August 2012

Abstract

In this paper, we study pathwise estimation of the global positive solutions for the stochastic functional Kolmogorov-type systems with infinite delay. Under some conditions, the growth rate of the solutions for such systems with general noise structures is less than a polynomial rate in the almost sure sense. To illustrate the applications of our theory more clearly, this paper also discusses various stochastic Lotka-Volterra-type systems as special cases.

MSC: 34K50, 60H10, 92D25, 93E03.

Keywords:
stochastic functional Kolmogorov systems; Lotka-Volterra systems; pathwise estimation; infinite delay