Ergodic properties for \alpha-CIR models and a class of generalized Fleming-Viot processes

摘要

We discuss a Markov jump process regarded as a variant of the CIR(Cox-Ingersoll-Ross) model and its infinite-dimensional extension. These modelsbelong to a class of measure-valued branching processes with immigration, whosejump mechanisms are governed by certain stable laws. The main result gives alower spectral gap estimate for the generator. As an application, a certainergodic property is shown for the generalized Fleming-Viot process obtained asthe time-changed ratio process.