Academic Report of School of Mathematical Sciences [2025] No. 128  

(Series Report for High-Level University Construction No. 1230)  

Title: Ergodicity of Conditional McKean–Vlasov Jump Diffusion  

Speaker: Professor Bao Jianhai (Tianjin University)  

Time: 9:30–10:30, November 21, 2025 (Friday)  

Location: Room 514, Huixing Building  

Abstract:  

In this talk, we are interested in conditional McKean–Vlasov jump diffusions, which are also termed as McKean–Vlasov stochastic differential equations with jump idiosyncratic noise and jump common noise. As far as conditional McKean–Vlasov jump diffusions are concerned, the corresponding conditional distribution flow is a measure-valued process, which indeed satisfies a stochastic partial integral differential equation driven by a Poisson random measure. Via a novel construction of the asymptotic coupling by reflection, we explore the ergodicity of the underlying measure-valued process corresponding to a one-dimensional conditional McKean–Vlasov jump diffusion when the associated drift term fulfills a partially dissipative condition with respect to the spatial variable. In addition, the theory derived demonstrates that the intensity of the jump common noise and the jump idiosyncratic noise can simultaneously enhance the convergence rate of the exponential ergodicity.  

Speaker Biography:  

Bao Jianhai is a Professor and Doctoral Supervisor at the Center for Applied Mathematics, Tianjin University. He received his Ph.D. from Swansea University, UK, in 2013. From 2013 to 2020, he worked at the School of Mathematics and Statistics, Central South University, and joined the Center for Applied Mathematics at Tianjin University in June 2020.  

All faculty and students are welcome!  

Host: Dong Hailing  

School of Mathematical Sciences  

November 20, 2025