题    目：Functional inequalities for stable jump diffusions

主讲人：王涛 讲师

单    位：江苏师范大学

时    间：2025年12月13日 9:00

地    点：数学院二楼会议室

摘    要：In this talk, we establish necessary and sufficient conditions for various of functional inequalities of onedimensional stable jump diffusions. Combined with the authors’ previous findings, these results collectively construct a stability diagram analogous to that of one-dimensional diffusion processes and birth-death processes. The tools we employ include the variational formula for Dirichlet eigenvalues, the construction and estimation of harmonic functions and killed Green functions, the fractional Hardy inequality, and the construction of Lyapunov function sequences. Finally, we will also discuss the feasibility of this problem for general symmetric L´evy processes and explore functional inequalities from the perspective of capacity.

简    介：王涛，2017年本科毕业于西安交通大学，2023年博士毕业于北京师范大学。现任教于江苏师范大学，主要研究兴趣是马氏过程的稳定性和非局部狄氏型的泛函不等式，在Bernoulli, SPA，JTP等期刊发表文章若干。