On backward stochastic differential equations driven by Gaussian noise

报告题目

On backward stochastic differential equations driven by Gaussian noise

报 告 人

北京师范大学—香港浸会大学联合国际学院

吴奖伦 教授

报告时间

2025年10月19日（周日）下午16：30-18：30

报告地点

上海师范大学徐汇校区西区3号楼3楼会议室332

报告摘要

We are concerned with backward stochastic differential equations (BSDEs) and distribution dependent backward stochastic differential equations (DDBSDEs) driven by Gaussian noise. We first present upper and lower non-Gaussian bounds for the densities of the marginal laws of solutions to BSDEs driven by fractional Brownian motions. Then, we derive Gaussian estimates for the densities of BSDEs driven by a Gaussian process in the manner that the solution can be established via an auxiliary BSDE driven by a Brownian motion. As for DDBSDEs driven by Gaussian noise, after establishing the existence and uniqueness results, we show a comparison theorem and a new representation for DDBSDEs (which is even new for the case of the equations driven by Brownian motion). The obtained representation then leads to a novel converse comparison theorem. Finally, we derive transportation inequalities and Log-Sobolev inequalities via the stability of the Wasserstein distance and the relative entropy of measures under the homeomorphism condition. Talk is based on joint work with Xiliang Fan (Anhui Normal University).