Processus de L{\'e}vy avec changements de rythmes

Abstract

This paper introduces Switching Processes, called SP. Their constructions are inspired by the PDMP's ones (PDMP stands for Piecewise Deterministic Markov Process). A Markov process, called the intrinsic process, replaces the PDMP's flow. Jumps are added ; they occur randomly as their locations ; their distributions depend on the process's trajectory between them. When the intrinsic process is a Levy process, thanks to its L{\'e}vy-It{\^o} decomposition as a semi-martingale, we obtain the expected Kolmogorov equations for the SP. The results are extended to It{\^o}-L{\'e}vy processes, in particular to diffusion processes.