We consider the long-term properties of a stochastic SVIR epidemic model with saturation
incidence rates and logistic growth in this paper. We firstly derive the fitness of a unique …

Abstract This work (Part (I)) together with its companion (Part (II)) develops a new framework
for stochastic functional Kolmogorov equations, which are nonlinear stochastic differential …

This paper is focused on analysis of Euler–Maruyama-type approximations for stochastic
functional differential equations with impulsive perturbations and Markovian switching. The …

This paper devotes to the study of a Lotka–Volterra model which has one prey and two
predators with nonlinear stochastic perturbations and distributed delay. It is first proved that …

Motivated by the traditional Lotka-Volterra competitive models, this paper proposes and
analyzes a class of stochastic reaction-diffusion partial differential equations. In contrast to …

Focusing on a class of regime-switching functional diffusion processes with infinite delay, a
Freidlin–Wentzell type large deviations principle (LDP) is established by using an extended …

In this paper, two stochastic vegetation-water dynamic systems are proposed and studied.
First, for the deterministic system, the possible equilibria and the related local stability are …

This paper presents Part I of a two-part series on studying the long-term coexistence states
of stochastic generalized Kolmogorov systems with small diffusion. Part I establishes a …

Since it is difficult to implement implicit schemes on the infinite-dimensional space, we aim to
develop the explicit numerical method for approximating super-linear stochastic functional …

This work examines a class of path-dependent stochastic systems which are hybrid with
wideband noise, Poisson jumps and a singularly perturbed Markov chain. The addition of …