报告题目：Stable Levy-type processes: symmetry, ergodicity, QSDs and functional inequalities
时 间：2024年1月24日（星期三）11：00
地 点：科研楼18号楼1102
主 办：数学与统计学院
参加对象：概率统计系及其他感兴趣的师生
报告摘要：First, we provide the sufficient and necessary conditions for the symmetry of the following $\alpha$-stable L\'evy-type operator $\mathcal{L}$ on $\mathbb{R}$:
$$\mathcal{L}=a(x){\Delta^{\alpha/2}}+b(x)\frac{\d}{\d x},$$
where $a,b$ are the continuous positive and differentiable functions, respectively.
Under the assumption of symmetry, we further study the criteria for ergodicity and functional inequalities (including Poincar\'e/super-Poincar\'e inequalities, logarithmic Sobolev inequalities and Nash inequalities).
The results above are qualitatively sharp in the sense that they still hold true in the case $\alpha=2$. As applications, we also prove the compactness and QSDs for killed semigroups.
报告人简介：江苏师范大学讲师。2017年本科毕业于西安交通大学数学与统计学院数学试验班(珠峰计划), 2020年硕士毕业于北京师范大学, 2023年博士毕业于北京师范大学，概率论与数理统计专业。已在 Bernoulli, Stochastic Process. Appl., J. Theoret. Probab, J. Appl. Probab. 等国内外SCI杂志上发表论文数篇.