Speaker: Peter Friz, TU and WIAS Berlin Professor. Professor Friz is a leading researcher in stochastic analysis and rough path theory, areas that lie at the intersection of probability, analysis, and applications such as finance and stochastic dynamics. He completed his PhD at the Courant Institute in New York and has since made major contributions to our understanding of irregular stochastic systems. He currently leads the DFG Collaborative Research Centre on Rough Analysis and Stochastic Dynamics, and his work continues to shape how we model randomness in complex systems.

Date: October 10, 2025

Time: 16:30 pm

Location: E119, Huagang East Building, Shandong University Qingdao Campus

Sponsor: Research Center for Mathematics and Interdisciplinary Sciences, Shandong University

Abstract:

The theory of rough stochastic differential equations (arXiv:2106.10340) is applied to revisit classical problems in stochastic filtering. We provide rough counter-parts to the Kallianpur-Striebel formula and the Zakai and Kushner-Stratonovich equations, seen to coincide with classical objects upon randomization. We follow Crisan-Pardoux (arXiv:2411.11125) in doing so in a correlated diffusion setting. Well-posedness of the (rough) filtering equation is seen to hold under dimension-independent regularity assumption, in contrast to the stochastic case. In a final part, we discuss rough extended Kalman filters, with conditionally Gaussian statistics, whose characteristics evolve along Riccati rough differential equations. (Joint work with Fabio Bugini, Khoa Lê, Huilin Zhang)

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/206604.htm