報(bào) 告 人：邱志鵬 教授

報(bào)告題目：Quasi-stationary distributions for absorbed diffusions driven by a class of Markov processes

報(bào)告時(shí)間：2025年3月15日（周六）下午3:30

報(bào)告地點(diǎn)：靜遠(yuǎn)樓1508會(huì)議室

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

      邱志鵬，南京理工大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院教授、博士生導(dǎo)師。主要從事常微分方程、動(dòng)力系統(tǒng)與生物數(shù)學(xué)的研究工作，主持國家自然科學(xué)基金4項(xiàng)，國家自然科學(xué)基金國際合作基金1項(xiàng)，教育部留學(xué)回國基金1項(xiàng)，參加國家自然科學(xué)基金面上項(xiàng)目2項(xiàng)和江蘇省自然科學(xué)基金青年項(xiàng)目1項(xiàng)，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(fā)表論文多篇，曾先后訪問過美國Purdue大學(xué)、Florida大學(xué)，意大利Trento大學(xué)、加拿大York大學(xué)和Alberta大學(xué)。

報(bào)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.