Kolmogorov-type systems with regime-switching jump diffusion perturbations

Fuke Wu*, George Yin, Zhuo Jin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

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 pth moment. Finally, this paper also considers a stochastic Lotka-Volterra system with regime-switching jump diffusion processes as a special case.

Original languageEnglish
Pages (from-to)2293-2319
Number of pages27
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume21
Issue number7
DOIs
Publication statusPublished - Sept 2016
Externally publishedYes

Keywords

  • Bounedeness
  • Brownian motion
  • Extinction
  • Global solution
  • Jump process
  • Kolmogorov-type system
  • Regime switching

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