报告题目：On the extinction-extinguishing dichotomy for a stochastic Lotka-Volterra type population dynamical system

报 告 人：杨叙 副教授 北方民族大学

邀请人：李童庆、薄立军

报告时间：2022年12月4日（周日）10:00-11:30

腾讯会议ID：120-533-026，密码：2022

报告人简介：杨叙，北方民族大学副教授。2013年博士毕业于北京师范大学，主要从事分枝过程、随机微分方程和随机偏微分方程方面的研究工作，近5年在《Annals of Applied Probability》、《Stochastic Processes and their Applications》和《Journal of Differential Equations》等期刊上发表过多篇学术论文，主持或完成国家自然科学基金青年项目1项、面上项目1项和地区项目1项。

报告摘要：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 L\'evy 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.

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