  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.
