Poisson approximation of increment processes with
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 726-742 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we present weak convergence results for Markov switched increment processes toward a compound Poisson process. The switching Markov process is considered also with an asymptotic split phase space. These results are obtained by a semimartingale approach.
Keywords: semimartingale, Markov process, weak convergence, compound Poisson process, merging scheme.
Mots-clés : increment process
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V. S. Korolyuk; N. Limnios. Poisson approximation of increment processes with. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 726-742. http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a5/

[1] Anisimov V. V., “Switching processes: averaging principle, diffusion approximation and applications”, Acta Appl. Math., 40:2 (1995), 95–141 | DOI | MR | Zbl

[2] Billingsli P., Skhodimost veroyatnostnykh mer, Nauka, M., 1977, 352 pp. | MR

[3] Borovskikh Yu. V., Korolyuk V. S., Martingale Approximation, VSP, Utrecht, 1997, 322 pp. | MR | Zbl

[4] Çinlar E., Jacod J., Protter P., Sharpe M. J., “Semimartingale and Markov processes”, Z. Wahrscheinlichkeitstheor. verw. Geb., 54:2 (1980), 161–219 | DOI | MR

[5] Ethier S. N., Kurtz T. G., Markov Processes: Characterization and Convergence, Wiley, New York, 1986, 534 pp. | MR | Zbl

[6] Gut A., Stopped Random Walks, Springer-Verlag, New York, 1988, 199 pp. | MR

[7] Zhakod Zh., Shiryaev A. N., Predelnye teoremy dlya sluchainykh protsessov, v. 1, 2, Fizmatlit, M., 1994, 544 pp. ; 368 с. | MR

[8] Kluppelberg C., Mikosch T., “Explosive Poisson shot noise processes with applications to risk reserves”, Bernoulli, 1:1–2 (1995), 125–142 | DOI | MR

[9] Korolyuk V. S., Korolyuk V. V., Stochastic Models of Systems, Kluwer, Dordrecht, 1999, 185 pp. | MR

[10] Korolyuk V. S., Limnios N., “A singular perturbation approach for Liptser's functional limit theorem and some extensions”, Theory Probab. Math. Statist., 58 (1998), 76–80 | MR | Zbl

[11] Korolyuk V. S., Limnios N., “Diffusion approximation of integral functionals in merging and averaging scheme”, Theory Probab. Math. Statist., 59 (1999), 101–107 | MR

[12] Korolyuk V. S., Limnios N., “Diffusion approximation of integral functionals in double merging and averaging scheme”, Theory Probab. Math. Statist., 60 (2000), 87–94 | MR

[13] Liptser R. Sh., Shiryaev A. N., Teoriya martingalov, Nauka, M., 1986, 512 pp. | MR | Zbl

[14] Liptser R. Sh., Shiryaev A. N., “Martingaly i predelnye teoremy dlya sluchainykh protsessov”, Itogi nauki i tekhniki, sovr. problemy matem., fundam. napr., 45, 1989, 159–253

[15] Osaki S., Stochastic System Reliability Modeling, World Scientific, Singapore, 1985, 285 pp. | MR | Zbl

[16] Parzen E., Stochastic Processes, SIAM, Philadelphia, 1999, 324 pp. | MR | Zbl

[17] Prabhu N. U., Stochastic Storage Processes, Springer-Verlag, New York, Berlin, 1980, 140 pp. | MR | Zbl

[18] Stroock D. W., Varadhan S. R. S., Multidimensional Diffusion Processes, Springer-Verlag, Berlin, New York, 1979, 338 pp. | MR | Zbl

[19] Sviridenko M. N., “Martingalnaya kharakterizatsiya predelnykh raspredelenii v prostranstve funktsii bez razryvov vtorogo roda”, Matem. zametki, 43:5 (1988), 692–703 | MR