English

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

Probability 2017-01-19 v1

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.

Keywords

Cite

@article{arxiv.1701.05085,
  title  = {Processus de L{\'e}vy avec changements de rythmes},
  author = {Christiane Cocozza-Thivent},
  journal= {arXiv preprint arXiv:1701.05085},
  year   = {2017}
}

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in French

R2 v1 2026-06-22T17:53:15.855Z