Differential Equations with Small Stochastic Terms Under the Lévy Approximating Conditions
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We propose new methods for the investigation of a model of stochastic evolution with Markov switchings capable of separation of the diffusion component and big jumps of the perturbing process in the limiting equation. Big jumps of this type may describe seldom catastrophic events in various applied problems. We consider the case where the system is perturbed by an impulsive process in the nonclassical approximation scheme. Special attention is given to the asymptotic behavior of the generator of the analyzed evolutionary system.
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- 1.J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes, Springer, Berlin (2003).Google Scholar
- 2.V. S. Korolyuk and V. V. Korolyuk, Stochastic Models of Systems, Kluwer, Dordrecht (1999).Google Scholar
- 5.G. Papanicolaou, D. Stroock, and S. R. S. Varadhan, “Martingale approach to some limit theorems,” in: Duke Turbulence Conference (Durham, NC, April 23–25, 1976): Duke Univ. Math. Ser. III, Duke University, New York (1977).Google Scholar
- 7.S. A. Semenyuk and Ya. M. Chabanyuk, “Stochastic evolutionary systems with impulsive perturbations,” Visn. Nats. Univ. “L’vivs’ka Politekhnika,” Ser. Fiz.-Mat. Nauk, Issue 660, 56–60 (2009).Google Scholar
- 8.Ya. M. Chabanyuk, “Approximation by diffusion processes in the averaging scheme,” Dop. Nats. Akad. Nauk Ukr., No. 12, 35–40 (2004).Google Scholar
- 9.A.V. Nikitin and U. T. Khimka, “Asymptotics of normalized control with Markov switchings,” Ukr. Math. Zh., 68, No. 8, 1092–1101 (2016); English translation : Ukr. Math. J., 68, No. 8, 1252–1262 (2017).Google Scholar