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

2013/07/09 by Kenji Handa, Handa, Kenji
Economics, Econometrics and Finance · Mathematics · #60J75 (Primary) 60G57 (Secondary) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1307.2407

openalex publication_date 2013/07/09 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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.

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