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

TL;DR

This paper investigates ergodic properties of IR models and generalized Fleming-Viot processes, providing spectral gap estimates and demonstrating ergodicity in measure-valued branching processes with stable law-driven jumps.

Contribution

It introduces a spectral gap estimate for IR models and extends ergodic analysis to a class of infinite-dimensional measure-valued processes.

Findings

Lower spectral gap estimate established for the generator.

Ergodic properties demonstrated for the generalized Fleming-Viot process.

Models involve stable law-driven jump mechanisms.

Abstract

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