杨叙 副教授（10 Feb. 2023）.pdf

应用数学讲座 Научный Семинар по Прикладной Математике Research Seminar on Applied Mathematics 应用数学报告（75） 报告人 / Докладчик / Speaker: 杨叙 副教授（北方民族大学） 题目 / Название / Title: A general continuous-state nonlinear branching process 时间 / Время / Time：10 Feb. 2023, 8:00-12:00 地点 / Место / Venue: 腾讯会议：140-462-177 摘要 / Аннотация / Abstract: we consider the unique nonnegative solution to the following generalized version of the stochastic differential equation for a continuous-state branching process: where W(dt, du) and N(ds, dz, du) denote a Gaussian white noise and an independent spectrally positive Poisson random measure, respectively, and γ_0,γ_1 and γ_2 are functions on R^+ with both γ_1 and γ_2 taking nonnegative values. Intuitively, this process can be identified as a continuousstate branching process with population-size-dependent branching rates and with competition. Using martingale techniques we find rather sharp conditions on extinction, explosion and coming down from infinity behaviors of the process. Some Foster– Lyapunov-type criteria are also developed for such a process. More explicit results are obtained when γ_i , i = 0, 1,2 are power functions. 访问学者以及需要做报告的学者请联系 张晔 教授 / Всем желающим выступить с докладами на семинаре просьба обращаться к Чжану Е ye.zhang@smbu.edu.cn