報 告 人：邱志鵬 教授

報告題目：Quasi-stationary distributions for absorbed diffusions driven by a class of Markov processes

報告時間：2025年3月15日（周六）下午3:30

報告地點：靜遠樓1508會議室

主辦單位：數學與統計學院、數學研究院、科學技術研究院

報告人簡介：

      邱志鵬，南京理工大學數學與統計學院教授、博士生導師。主要從事常微分方程、動力系統與生物數學的研究工作，主持國家自然科學基金4項，國家自然科學基金國際合作基金1項，教育部留學回國基金1項，參加國家自然科學基金面上項目2項和江蘇省自然科學基金青年項目1項，目前已在Bull. Math. Biol., Math. Biosci., J. Diff. Equs., SIAM J. Appl. Math., J. Math. Biol., J. Theor. Biol.等期刊上發表論文多篇，曾先后訪問過美國Purdue大學、Florida大學，意大利Trento大學、加拿大York大學和Alberta大學。

報告摘要：

      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.