Kolmogorov-type systems with regime-switching jump diffusion perturbations

Fuke  Wu; George Yin; Zhuo  Jin

doi:10.3934/dcdsb.2016048

Article Contents

2016, Volume 21, Issue 7: 2293-2319. Doi: 10.3934/dcdsb.2016048

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Kolmogorov-type systems with regime-switching jump diffusion perturbations

1.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074
2.
Department of Mathematics, Wayne State University, Detroit, Michigan 48202
3.
Centre for Actuarial Studies, Department of Economics, The University of Melbourne, VIC 3010

Received: July 31, 2015

Revised: October 31, 2015

Published: August 2016

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Abstract

Population systems are often subject to various different types of environmental noises. This paper considers a class of Kolmogorov-type systems perturbed by three different types of noise including Brownian motions, Markovian switching processes, and Poisson jumps, which is described by a regime-switching jump diffusion process. This paper examines these three different types of noises and determines their effects on the properties of the systems. The properties to be studied include existence and uniqueness of global positive solutions, boundedness of this positive solution, and asymptotic growth property, and extinction in the senses of the almost sure and the $p$th moment. Finally, this paper also considers a stochastic Lotka-Volterra system with regime-switching jump diffusion processes as a special case.

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Mathematics Subject Classification: Primary: 60H10, 60J70, 60J28; Secondary: 92D25, 93E03.

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