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

Kenji Handa (Saga University)

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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Pages: 1-25

Publication Date: July 24, 2014

DOI: 10.1214/EJP.v19-2928

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