- 控制理论和非线性滤波讨论班

Extension of the Kalman–Bucy Filter to Elementary Linear Systems with Fractional Brownian Noises

组织者

丘成栋

演讲者

康家熠

时间

2024年05月22日 15:00 至 15:30

地点

理科楼A-304

摘要

I will report a paper on investigating the optimal filtering problem in the simplest Gaussian linear system driven by fractional Brownian motions. At first they extend to this setting the Kalman–Bucy filtering equations which are well-known in the specific case of usual Brownian motions. Closed form Volterra type integral equations are derived both for the mean of the optimal filter and the variance of the filtering error. Then the asymptotic stability of the filter is analyzed. It is shown that the variance of the filtering error converges to a finite limit as the observation time tends to infinity.

演讲者介绍

Jiayi Kang received his Ph.D. in Mathematics from Tsinghua University in 2024. He joined the Beijing Institute of Mathematical Sciences and Applications (BIMSA) as an Assistant Researcher in July 2024, and became an Assistant Professor at the Hetao Institute for Mathematical and Interdisciplinary Sciences (HIMIS) in November 2025. His research focuses on the intersection of deep learning, nonlinear filtering, and computational biology. His main research interests include: neural network-based filtering algorithms and their mathematical foundations, sampling methods in Wasserstein geometry, nonlinear filtering theory (including the Yau-Yau method) and its applications in climate science and other fields, as well as computational genomics and evolutionary system modeling. He is committed to solving complex problems in science and engineering using mathematical and machine learning methods.