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.
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.
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@article{CRMATH_2016__354_7_723_0,
author = {Koroliuk, Volodymyr S. and Limnios, Nikolaos and Samoilenko, Igor V.},
title = {L\'evy and {Poisson} approximations of switched stochastic systems by a semimartingale approach},
journal = {Comptes Rendus. Math\'ematique},
pages = {723--728},
publisher = {Elsevier},
volume = {354},
number = {7},
year = {2016},
doi = {10.1016/j.crma.2016.04.008},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.crma.2016.04.008/}
}
TY - JOUR AU - Koroliuk, Volodymyr S. AU - Limnios, Nikolaos AU - Samoilenko, Igor V. TI - Lévy and Poisson approximations of switched stochastic systems by a semimartingale approach JO - Comptes Rendus. Mathématique PY - 2016 SP - 723 EP - 728 VL - 354 IS - 7 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2016.04.008/ DO - 10.1016/j.crma.2016.04.008 LA - en ID - CRMATH_2016__354_7_723_0 ER -
%0 Journal Article %A Koroliuk, Volodymyr S. %A Limnios, Nikolaos %A Samoilenko, Igor V. %T Lévy and Poisson approximations of switched stochastic systems by a semimartingale approach %J Comptes Rendus. Mathématique %D 2016 %P 723-728 %V 354 %N 7 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2016.04.008/ %R 10.1016/j.crma.2016.04.008 %G en %F CRMATH_2016__354_7_723_0
Koroliuk, Volodymyr S.; Limnios, Nikolaos; Samoilenko, Igor V. 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://www.numdam.org/articles/10.1016/j.crma.2016.04.008/
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