Stochastic Population Dynamics Driven by Levy Noise

TL;DR

This paper investigates stochastic population models influenced by Levy noise, establishing solution existence and uniqueness, and analyzing their long-term behavior using advanced probabilistic techniques.

Contribution

It introduces a novel application of the Khasminskii-Mao theorem and exponential martingale inequalities to Levy-driven population dynamics models.

Findings

Existence of a unique global positive solution

Asymptotic pathwise estimation of the model

Application of advanced stochastic analysis techniques

Abstract

This paper considers stochastic population dynamics driven by Levy noise. The contributions of this paper lie in that (a) Using Khasminskii-Mao theorem, we show that the stochastic differential equation associated with the model has a unique global positive solution; (b) Applying an exponential martingale inequality with jumps, we discuss the asymptotic pathwise estimation of such model.