Comptes Rendus
no. 7
Probability theory
Lévy and Poisson approximations of switched stochastic systems by a semimartingale approach
[Approximations de Lévy et de Poisson des systèmes stochastiques modulés, via une approche basée sur les semi-martingales]

Présenté par : Paul Deheuvels

Volodymyr S. Koroliuk1 ; Nikolaos Limnios2 ; Igor V. Samoilenko1
1 Institute of Mathematics, Ukrainian National Academy of Science, Kyiv, Ukraine
2 Laboratoire de mathématiques appliquées, Université de technologie de Compiègne, Sorbonne universités, France
Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 723-728.

Nous étudions dans cette Note la convergence faible des fonctionnelles additives des processus à accroissements localement indépendants, avec modulation markovienne, vers des processus de Lévy et de Poisson, sous différentes hypothèses et rééchelonnements de temps. Nous utilisons des techniques de perturbation singulière des opérateurs pour établir des résultats de convergence faible concernant les caractéristiques prédictibles des semi-martingales.

In this Note, we present the weak convergence of additive functionals of processes with locally independent increments and Markov switching in Lévy and Poisson approximation schemes. The singular perturbation problem for the generators of switched processes is used to prove the semimartingales' predictable characteristics convergence.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.04.008
Volodymyr S. Koroliuk 1 ; Nikolaos Limnios 2 ; Igor V. Samoilenko 1

1 Institute of Mathematics, Ukrainian National Academy of Science, Kyiv, Ukraine
2 Laboratoire de mathématiques appliquées, Université de technologie de Compiègne, Sorbonne universités, France 
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Volodymyr S. Koroliuk; Nikolaos Limnios; Igor V. Samoilenko. Lévy and Poisson approximations of switched stochastic systems by a semimartingale approach. Comptes Rendus. Mathématique, Volume 354 (2016) no. 7, pp. 723-728. doi : 10.1016/j.crma.2016.04.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.04.008/

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[9] V.S. Koroliuk; N. Limnios; I.V. Samoilenko Lévy approximation of processes with locally independent increments with semi-Markov switching, Ukr. Math. Bull., Volume 6 (2009) no. 3, pp. 371-384

[10] V.S. Koroliuk; N. Limnios; I.V. Samoilenko Poisson approximation of process with locally independent increments and semi-Markov switching – toward application in reliability (M.S. Nikulin; N. Limnios; N. Balakrishnan; W. Kahle; C. Huber-Carol, eds.), Advances on Degradation Models with Application to Reliability, Survival Analysis and Finance, Birkhäuser, 2010, pp. 105-116

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