报告题目：Zero Noise Selection of Multidimensional Peano Phenomena
报告人：张良泉（中国⼈⺠⼤学）
邀请人：宗高峰副教授
主持人：李娜教授统计与数学学院副院长
报告地点：燕山校区1号教学楼1502
报告时间：2023年10月18日（周三）10：30—11：30
主办单位：山东财经大学统计与数学学院
摘要：For the ordinary differential equation (ODE in short), there is a general local existence theory if the drift is only supposed to be continuous (Peano's theorem), even though uniqueness may fail in this case. However, the perturbed stochastic differential equation (SDE in short) has a unique strong solution when the drift is assumed to be continuous and bounded. Moreover, when the noise intensity tends to zero, the solutions to the perturbed SDEs converge, in a suitable sense, to the solutions of the ODE. This phenomenon has been extensively studied for one-dimensional case in literature. The goal of present paper is to analyze some multi-dimensional cases. When the drift has an isolated zero and is non Lipschitz continuous at zero, the ODE may have infinitely many solutions. Our main result shows which solutions of the ODE can be the limits of the solutions of the SDEs by stopping time technique. The main novelty consists in the treatment of multi-dimensional case in a simple manner.
报告人简介：张良泉副教授，本科毕业于⼭东⼤学，博⼠毕业于法国⻄部列塔尼⼤学与⼭东⼤学，法国国家信息与⾃动化研究院做博⼠后。⽬前在中国⼈⺠⼤学数学学院⾦融数学系担任系主任。以第⼀作者在Automatica、JDE、ESAIM等期刊发表20多篇论⽂，在科学出版社出版专著⼀部，解决多个控制领域相关问题。多次访问⾹港城市⼤学、⾹港理⼯⼤学。2019年6⽉受邀参加第⼋届华⼈数学家⼤会。⽬前承担⾃然基⾦⾯上项⽬⼀项，中国⼈⺠⼤学创新基⾦⼀项，结题三项。教育部学位与研究⽣教育发展中⼼、国家⾃然科学基⾦、国家留学基⾦委公派留学评审专家，⼭东省⾃然科学技术⼆等奖（第四位）。主要研究领域：随机控制、⾦融数学、噪声摄动、卡尔曼滤波稳定性等。