報(bào) 告 人：宋仁明 教授

報(bào)告題目：Approximate factorizations for non-symmetric jump processes

報(bào)告時(shí)間：2025年6月18日（周三）下午4:00

報(bào)告地點(diǎn)：泉山校區(qū)5號(hào)樓107

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

報(bào)告人簡(jiǎn)介：

   宋仁明，美國(guó)Illinois大學(xué)教授，1986年河北大學(xué)碩士畢業(yè)，1989年美國(guó)Florida大學(xué)博士畢業(yè)。訪(fǎng)問(wèn)過(guò)德國(guó)、法國(guó)、日本、韓國(guó)和臺(tái)灣等國(guó)家和地區(qū)的20余所大學(xué)和研究所。從事隨機(jī)過(guò)程和隨機(jī)分析研究，在《Trans. Amer. Math. Soc.》、《Proc. London Math. Soc.》、《J. European Math. Soc》、《Math. Ann.》、《J. Funct. Anal.》、《Ann. Probab.》、《Probab. Th. Rel. Fields》、《Stoch. Proc. Appl.》等數(shù)學(xué)、概率國(guó)際權(quán)威刊物上發(fā)表論文160余篇；多次在國(guó)際學(xué)術(shù)會(huì)議上作邀請(qǐng)報(bào)告。

報(bào)告摘要：

      In this talk, I will talk about a recent paper with Soobin Cho. In this paper, we first extend the approximate factorization for purely discontinuous Markov processes established by Cho-Kim-Song-Vondracek in 2020 by getting rid of some of the conditions. Then we apply the approximate factorization to obtain two-sided heat kernel estimates for three classes of processes: stable-like processes with stable killings in $C^{1, Dini}$ open sets; killed stable-like processes in the setting of the recent preprint  by Kim-Weidner in $C^{1, \epsilon}$ open sets; and non-symmetric stable processes in what we call $C^{1, 2-Dini}$ open sets. In particular, we obtain explicit sharp two-sided heat kernel estimates of killed $\alpha$-stable processes in $C^{1, Dini}$ open sets for all $\alpha\in (0, 2)$ and of censored $\alpha$-stable processes in $C^{1, Dini}$ open sets for $\alpha\in (1, 2)$.