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arXiv · 1701.05085

Processus de L{é}vy avec changements de rythmes

Christiane Cocozza-Thivent
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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{é}vy-It{ô} decomposition as a semi-martingale, we obtain the expected Kolmogorov equations for the SP. The results are extended to It{ô}-L{é}vy processes, in particular to diffusion processes.

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Christiane Cocozza-Thivent. 2017-01-18. Processus de L{é}vy avec changements de rythmes. https://arxiv.org/abs/1701.05085

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