報 告 人：陳振慶 教授

報告題目：Boundary Harnack principle for diffusion processes with jumps

報告時間：2024年11月20日（星期三）下午3：30

報告地點：靜遠樓1506學術報告廳

主辦單位：數學研究院、數學與統計學院、科學技術研究院

報告人簡介：

       陳振慶，美國華盛頓大學（西雅圖）數學系教授，分別于2007年和2014年當選為美國數理統計學會士(Fellow)和美國數學學會會士(Fellow)。陳振慶教授主要從事概率論及隨機過程的研究，主要的研究方向包括概率論以及隨機分析，馬爾可夫過程以及狄氏空間理論，隨機微分方程，擴散過程，穩定過程以及偏微分方程中的概率方法等。發表學術論文200余篇，學術專著兩部，國際期刊Potential Analysis的主編，2019年獲伊藤獎 (Ito Prize)。

報告摘要：

       The classical boundary Harnack principle asserts that two positive harmonic functions that vanish on a portion of the boundary of a smooth domain decay at the same rate. It is well known that scale invariant boundary Harnack inequality holds for Laplacian \Delta on uniform domains and holds for fractional Laplacians \Delta^s on any open sets. It has been an open problem whether the scale-invariant boundary Harnack inequality holds on bounded Lipschitz domains for Levy processes with Gaussian components such as the independent sum of a Brownian motion and an isotropic stable process (which corresponds to \Delta + \Delta^s).   

       In this talk, I will present a necessary and sufficient condition for the scale-invariant boundary Harnack inequality to hold for a class of diffusion processes with jumps on metric measure spaces. This result will then be applied to give a sufficient geometric condition for the scale-invariant boundary Harnack inequality to hold for subordinate Brownian motions having Gaussian components on bounded Lipschitz domains in Euclidean spaces. This condition is almost optimal and a counterexample will be given showing that the scale-invariant BHP may fail on some bounded Lipschitz domains with large Lipschitz constants. Based on joint work with Jieming Wang.