Geodesic
Poisson approximation of processes with locally independent increments with Markov switching
Teoriâ slučajnyh processov, Tome 15 (2009) no. 1, pp. 40-48

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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: semimartingale, Markov process, locally independent increments process, piecewise deterministic Markov process, weak convergence
Mots-clés : Poisson approximation, singular perturbation. 
@article{THSP_2009_15_1_a4,
     author = {V. S. Koroliuk and N. Limnios},
     title = {Poisson approximation of processes with locally independent increments with {Markov} switching},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {40--48},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2009_15_1_a4/}
}
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V. S. Koroliuk; N. Limnios. Poisson approximation of processes with locally independent increments with Markov switching. Teoriâ slučajnyh processov, Tome 15 (2009) no. 1, pp. 40-48. http://geodesic.mathdoc.fr/item/THSP_2009_15_1_a4/