# Event № 2403

Event № 2403

TE
Seminar in Probability and Stochastic Processes
- Zenghu Li (Beijing Normal University)
12/11/2019, Tuesday, 11:30

Type: Seminar

Name: Seminar in Probability and Stochastic Processes

Title: Ergodicities and exponential ergodicities of branching processes with immigration

Speaker: Zenghu Li (Beijing Normal University)

Place:
Meyer building (electrical engineering), room 861, Technion

*Abstract:*

Abstract: Under natural assumptions, we prove the ergodicities and exponential ergodicities in Wasserstein and total variation distances of Dawson-Watanabe superprocesses without or with immigration. Those processes are infinite-dimensional generalizations of the well-known continuous-state branching processes, which are also known as Cox-Ingersoll-Ross type models and have played important roles in the study of mathematical finance. The strong Feller property of the processes in the total variation distance is derived as a by-product. The key of our approach is a set of estimates for the variations of the transition probabilities. The estimates in Wasserstein distance are derived from an upper bound of the kernels induced by the first moment of the superprocess. Those in total variation distance are based on a comparison of the cumulant semigroup of the superprocess with that of a continuous-state branching process. The results improve and extend considerably those of Stannat (2003a, 2003b) and Friesen (2019+). We also show a connection between the ergodicities of the associated immigration superprocesses and decomposable distributions.

SubmittedBy:
Ron Rosenthal , ron.ro@technion.ac.il

EventLink: Event № 2403