We perform the asymptotic analysis of the problem of large deviations for impulsive processes in the scheme of Poisson approximation. Large deviations for impulsive processes in the scheme of Poisson approximation are determined by the exponential generator of a jump process with independent increments.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
S. N. Ethier and T. G. Kurtz, Markov Processes: Characterization and Convergence, Wiley, New York (1986).
J. Feng and T. G. Kurtz, Large Deviation for Stochastic Processes, American Mathematical Society, Providence, RI (2006).
M. J. Freidlin and A. D. Wentzel, Random Perturbation of Dynamical Systems, Springer, Berlin (1998).
J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes, Springer, Berlin (1987).
V. S. Koroliuk and N. Limnios, Stochastic Systems in Merging Phase Space, World Scientific, Singapore (2005).
V. S. Koroliuk, N. Limnios, and I. V. Samoilenko, “Poisson approximation of impulsive recurrent process with semi-Markov switching,” Stochast. Anal. Appl., 29, Issue 5, 769–778 (2011).
V. S. Korolyuk, “Markov random evolutions with independent increments in the scheme of asymptotically weak diffusion,” Dopov. Nats. Akad. Nauk Ukr., No. 6, 22–26 (2010).
V. S. Korolyuk, “Problem of large deviations for Markov random evolutions with independent increments in the scheme of asymptotically small diffusion,” Ukr. Mat. Zh., 62, No. 5, 643–650 (2010); English translation: Ukr. Math. J., 62, No. 5, 739–747 (2010).
A. A. Mogulskii, “Large deviation for processes with independent increments,” Ann. Probab., 21, 202–215 (1993).
I. V. Samoilenko, “Convergence of an impulsive storage process with jump switchings,” Ukr. Mat. Zh., 60, No. 9, 1283–1286 (2008); English translation: Ukr. Math. J., 60, No. 9, 1492–1497 (2008).
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 11, pp. 1526–1535, November, 2012.
About this article
Cite this article
Samoilenko, I.V. Large deviations for impulsive processes in the scheme of Poisson approximation. Ukr Math J 64, 1727–1738 (2013). https://doi.org/10.1007/s11253-013-0747-0
- Markov Process
- Asymptotic Analysis
- Jump Process
- Independent Increment
- Exponential Generator