Poisson approximation of processes with locally independent increments with Markov switching

V. S. Koroliuk^a, N. Limnios<sup>b

a</sup> Institute of Mathematics, Ukrainian National Academy of Science, Kiev, Ukraine
^b Laboratoire de Mathématiques Appliquées, Université de Technologie de Compiégne, France

Abstract: In this paper, the weak convergence of additive functionals of processes with locally independent increments and with Markov switching in the scheme of the Poisson approximation is proved. For the relative compactness, a method proposed by R. Liptser for semimartingales is used with a modification, where we apply a solution of a singular perturbation problem instead of the ergodic theorem.

Keywords: Poisson approximation, semimartingale, Markov process, locally independent increments process, piecewise deterministic Markov process, weak convergence, singular perturbation.

MSC: Primary 60J55, 60B10, 60F17, 60K10; Secondary 60G46, 60G60

Language: English

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