Kolmogorov-type systems with regime-switching jump diffusion perturbations

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.

Inverse optimal control of regime-switching jump diffusions

“…Inspired by problems of model complexity in random environments, in which both structural changes and sudden changes of parameters as well as large fluctuations coexist and are intertwined, this paper study regime-switching jump diffusion processes. The quantitative properties of these systems have greatly expanded over the previous few years, with most results making a connection between the control theory and the qualitative dynamics or long-time behavior of the associated dynamical system, see, for example, [5,17,18,19,20,21,22,23,25] and references therein.…”

Almost sure exponential stabilization and suppression by periodically intermittent stochastic perturbation with jumps

“…On the one hand, the approach of input feedback control with white noise has successfully stabilized a deterministic system. On the other hand, some authors have investigated almost sure stabilization and suppression of stochastic systems in terms of coefficient condition (see, e.g., [16,17,27,28,36]) and the references therein. It should be mentioned that these works in the literature we presented concentrate on the case of SDEs driven by classical Brownian motion.…”