Abstract
Ergodic theory is one of the central topics in the study of Markov processes. As an important class of Markov processes, branching processes have found interesting connections and widespread applications in several areas. In this talk, I will present some results on the ergodicity of continuous-state branching-type processes, including the existence and uniqueness of the stationary distribution, polynomial ergodicity, exponential ergodicity, and strong ergodicity. The main strategy involves the pathwise construction and analysis through Markov couplings based on strong solutions of stochastic equations.
