Poisson approximation of increment processes with Markov switching

Theory of Probability and its Applications

Volumn 49, Issue 4, 2004, Pages 629-644

  Korolyuk, V S ^a   Limnios, N ^b  

^a INSTITUTE OF HYDROBIOLOGY   (Ukraine)

^b UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

Compound poisson process; Increment process; Markov process; Merging scheme; Semimartingale; Weak convergence

Indexed keywords

EID: 30844437869     PISSN: 0040585X     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0040585X97981330     Document Type: Article

References (19)

1. V. V. ANISIMOV, Switching processes: Averaging principle, diffusion approximation and applications, Acta Appl. Math., 40 (1995), pp. 95-141.
2. P. BILLINGSLEY, Convergence of Probability Measures, John Wiley, New York, 1968.
3. YU. V. BOROVSKIKH AND V. S. KOROLYUK, Martingale Approximation, VSP, Utrecht, 1997.
4. E. ÇINLAR, J. JACOD, P. FROTTER, AND M. J. SHARPE, Semimartingale and Markov processes, Z. Wahrsch. Verw. Gebiete, 54 (1980), pp. 161-219.
5. S. N. ETHIER AND T. G. KURTZ, Markov Processes: Characterization and Convergence, John Wiley, New York, 1986.
6. A. GUT, Stopped Random Walks, Springer-Verlag, New York, 1988.
7. J. JACOD AND A. N. SHIRYAEV, Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin, 1987.
8. C. KLUPPELBERG AND T. MIKOSCH, Explosive Poisson shot noise processes with applications to risk reserves, Bernoulli, 1 (1995), pp. 125-142.
9. V. S. KOROLYUK AND V. V. KOROLYUK, Stochastic Models of Systems, Kluwer, Dordrecht, 1999.
10. V. S. KOROLYUK AND N. LIMNIOS, A singular perturbation approach for Liptser's functional limit theorem and some extensions, Theory Probab. Math. Statist., 58 (1998), pp. 76-80.
11. V. S. KOROLYUK AND N. LIMNIOS, Diffusion approximation of integral functionals in merging and averaging scheme, Theory Probab. Math. Statist., 59 (1999), pp. 101-107.
12. V. S. KOROLYUK AND N. LIMNIOS, Diffusion approximation of integral functional in double merging and averaging scheme, Theory Probab. Math. Statist., 60 (2000), pp. 87-94.
13. R. SH. LIPTSER AND A. N. SHIRYAYEV, Theory of Martingales, Kluwer, Dordrecht, The Netherlands, 1989.
14. R. SH. LIPTSER AND A. N. SHIRYAEV, Martingales and limit theorems for stochastic processes, in Encyclopaedia of Mathematical Sciences. Probability Theory III, Yu. V. Prokhorov and A. N. Shiryaev eds., Springer, Berlin, New York, pp. 158-247.
15. S. OSAKI, Stochastic System Reliability Modeling, World Scientific, Singapore, 1985.
16. E. PARZEN, Stochastic Processes, SIAM, Philadelphia, 1999.
17. N. U. PRABHU, Stochastic Storage Processes, Springer-Verlag, New York, Berlin, 1980.
18. D. W. STROOCK AND S. R. S. VARADHAN, Multidimensional Diffusion Processes, Springer-Verlag, Berlin, New York, 1979.
19. M. N. SVIRIDENKO, Martingale characterization of limit distributions in the space of functions without discontinuities of second kind, Math. Notes, 43 (1998), pp. 398-402.