Explicit numerical approximation for logistic models with regime switching in finite and infinite horizons

by   Xiaoyue Li, et al.

The stochastic logistic model with regime switching is an important model in the ecosystem. While analytic solution to this model is positive, current numerical methods are unable to preserve such boundaries in the approximation. So, proposing appropriate numerical method for solving this model which preserves positivity and dynamical behaviors of the model's solution is very important. In this paper, we present a positivity preserving truncated Euler-Maruyama scheme for this model, which taking advantages of being explicit and easily implementable. Without additional restriction conditions, strong convergence of the numerical algorithm is studied, and 1/2 order convergence rate is obtained. In the particular case of this model without switching the first order strong convergence rate is obtained. Furthermore, the approximation of long-time dynamical properties is realized, including the stochastic permanence, extinctive and stability in distribution. Some simulations and examples are provided to confirm the theoretical results and demonstrate the validity of the approach.


page 1

page 2

page 3

page 4


Explicit approximations for nonlinear switching diffusion systems in finite and infinite horizons

Focusing on hybrid diffusion dynamics involving continuous dynamics as w...

Strong convergence and asymptotic stability of explicit numerical schemes for nonlinear stochastic differential equations

In this article we introduce several kinds of easily implementable expli...

On the Poisson Stability to Study a Fourth-Order Dynamical System with Quadratic Nonlinearities

This article discusses the search procedure for the Poincaré recurrences...

An explicit approximation for super-linear stochastic functional differential equations

Since it is difficult to implement implicit schemes on the infinite-dime...

A positivity preserving numerical scheme for the mean-reverting alpha-CEV process

In this article, we present a method to construct a positivity preservin...