Financial Math Seminar

On the extinction-extinguishing dichotomy for a stochastic Lotka-Volterra type population dynamic system

  • 演讲者:杨旭(北方民族大学)

  • 时间:2022-05-06 10:00-11:00

  • 地点:腾讯会议 ID 703 7037 2992,密码 3804

Abstract:Applying the Foster-Lyapunov type criteria and a martingale method, we study a two-dimensional process $(X, Y)$ arising as the unique nonnegative solution to a pair of stochastic differential equations driven by independent Brownian motions and compensated spectrally positive Lévy random measures. Both processes $X$ and $Y$ can be identified as continuous-state nonlinear branching processes where the evolution of $Y$ is negatively affected by $X$. Assuming that process $X$ extinguishes, i.e. it converges to $0$ but never reaches $0$ in finite time, and process $Y$ converges to $0$, we identify rather sharp conditions under which the process $Y$ exhibits, respectively, one of the following behaviors: extinction with probability one, extinguishing with probability one or both extinction and extinguishing occurring with strictly positive probabilities. This talk is based on a joint work with Yan-Xia Ren, Jie Xiong and Xiaowen Zhou.