“数通古今，学贯中外”学术讲座第六十五期预告【王凤雨教授】

时间：4月15日（周二）下午3：30至4：30

地点：研究生楼103

报告人：王凤雨教授：北京师范大学教授

Title: Integration by Parts Formula and Shift Harnack Inequality for Stochastic Equations

Abstract: A new coupling argument is introduced to establish Driver's integration by parts formulaand shift Harnack inequality. Unlike known coupling methods where two marginal processes withdifferent starting points are constructed to move together as soon as possible, for the new-type coupling the two marginal processes start from the same point but their difference is aimed to reach a fixed quantity at a given time. Besides the integration by parts formula, the new coupling method is also efficient to imply the shift Harnack inequality. Differently from known Harnack inequalities where the values of a reference function at different points are compared, in the shift Harnack inequality the reference function, rather than the initial point, is shifted. A number of applications of the integration by parts and shift Harnack inequality are presented. The general results are illustrated by some concrete models including the stochastic Hamiltonian system where the associated diffusion process can be highly degenerate, delayed SDEs, and semi-linear SPDEs.