Generalized Poisson measures on topological spaces and applications

Abstract

We introduce and study a marked Poisson random measure on a σ-compact Hausdorff space. The underlying parameters of this measure are changing in accordance with the evolution of some stochastic process. This random measure (also known as a modulated measure) resembles those of the conventional Poisson random measure. Among many applications, the one about Poisson random measures modulated by semi-Markov processes found in stochastic finance.