报 告 人：邱志鹏 教授
报告题目：Quasi-stationary distributions for absorbed diffusions driven by a class of Markov processes
报告时间：2025年3月15日（周六）下午3:30
报告地点：静远楼1508会议室
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
邱志鹏，南京理工大学数学与统计学院教授、博士生导师。主要从事常微分方程、动力系统与生物数学的研究工作，主持国家自然科学基金4项，国家自然科学基金国际合作基金1项，教育部留学回国基金1项，参加国家自然科学基金面上项目2项和江苏省自然科学基金青年项目1项，目前已在Bull. Math. Biol., Math. Biosci., J. Diff. Equs., SIAM J. Appl. Math., J. Math. Biol., J. Theor. Biol.等期刊上发表论文多篇，曾先后访问过美国Purdue大学、Florida大学，意大利Trento大学、加拿大York大学和Alberta大学。
报告摘要：
The talk is devoted to present the transient dynamics of diffusion processes driven by a class of Markov processes, which is absorbed by the absorption set in finite time with probability one. Our primary concern is to analyze quasi-stationary distributions (QSDs) which characterize the long term behavior before absorption. Due to the irreversibility of the absorbed diffusion processes in this paper, probability methods are used to analyze the sub-Markovian semigroup generated by the absorbed diffusion processes. We provide the Lyapunov type criteria for the existence, uniqueness of the quasi-stationary distribution and show the exponential convergence to this QSD in the weighted total variation distance. Finally, the criteria is applied to stochastic ecological systems subject to both demographic and environmental stochasticity, and sufficient conditions are given for the existence, uniqueness and convergence of the quasi-stationary distribution. This work is jointed with Yu Zhu.
