A class of interacting marked point processes: rate of convergence to equilibrium

In this paper we obtain the rate of convergence to equilibrium of a class of interacting marked point processes, introduced by Kerstan, in two different situations. Indeed, we prove the exponential and subexponential ergodicity of such a class of stochastic processes. Our results are an extension of the corresponding results in a paper by Bremaud, Nappo and Torrisi (JAP, 2002). The generality of the dynamics which we take into account allows the application to the so-called loss networks, and multivariate birth-and-death processes.