数学学科2020系列学术报告之二

题目：Well-posedness of multi-dimensional degenerated SDEs
报告人：张伏
时间：2020年1月6日（周一）上午10:30-11:30
地点：1-301
报告人简介：张伏，现在上海理工大学理学院工作。2009年于南京大学数学系获理学硕士学位，研究方向为偏微分方程；2013年于复旦大学获理学博士学位，研究方向为随机控制。后在复旦大学管理学院从事金融数学方向博士后研究。现研究方向为随机控制、随机分析与偏微分方程。多篇文章在《SIAM J. Contrl. Optimal》、《Ann. Inst. Henri Poincaré Probab. Stat》、《Discrete and Continuous Dynamical Systems (A)》等学术杂志发表。
报告摘要：We consider a kind of SDEs degenerated at the boundary of a non-smooth domain. We prove uniqueness and existence of the martingale problem related to this degenerate SDEs under suitable  regularity conditions on the coefficients. Applying martingale problem theory of Stroock and Varadhan, we turn the uniqueness problem of the SDE into the well-posedness of a kind of degenerate PDE with Neumann boundary condition. The difficulties for solvability of the problem mainly are caused by the degeneration of the operator, domain with corner, and correlation of different components of the SDE. The Schauder estimate for the degenerate PDE is given.  This is a joint work with Kai Du.