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BIMSA Digital Economy Lab Seminar
BIMSA Digital Economy Lab Seminar
Convergence Analysis of Splitting Methods for Zakai Equations under α-Stable Lévy Noise
Convergence Analysis of Splitting Methods for Zakai Equations under α-Stable Lévy Noise
Organizers
Speaker
Jiayi Kang
Time
Friday, March 20, 2026 3:00 PM - 4:00 PM
Venue
A3-2-303
Online
Zoom 435 529 7909
(BIMSA)
Abstract
The Zakai equation describes the evolution of the unnormalized conditional density in nonlinear filtering. This paper studies nonlinear filtering for jump-diffusive systems whose state dynamics are driven by heavy-tailed, non-Gaussian α-stable Lévy processes, while the observations consist of mutually independent diffusion and jump components. To enable efficient computation, we approximate the Zakai equation via a splitting-up scheme on discrete time intervals, separating the prediction and update steps. Our main theoretical contribution is the extension of strong and weak convergence results for splitting-up approximations of the Zakai equation to filtering models with α-stable Lévy states and mixed-type observations. We further extend the Yau–Yau algorithm, originally developed for Gaussian filtering problems, to the α-stable Lévy setting. Numerical experiments on a highly nonlinear cubic sensor tracking problem demonstrate clear advantages of the proposed method over the sequential importance resampling particle filter.
Speaker Intro
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.