Differential Equations with Small Stochastic Additions Under Poisson Approximation Conditions
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The methods proposed in the paper allow us to investigate the model of stochastic evolution, which includes Markov switchings, and to identify big jumps of disturbing process in the limiting equation. Big jumps of this type may describe rare catastrophic events in different applied problems. We consider the case where system disturbance is defined by impulse process in nonclassical approximation scheme. Particular attention is paid to the asymptotic behavior of the generator of the evolutionary system under examination.
Keywordsstochastic diffusion equation generator on Banach space Markov process stochastic approximation procedure Poisson approximation
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- 8.S. A. Semenyuk and Ya. M. Chabanyuk, “Stochastic evolutionary systems with impulse perturbation,” Visnyk Natsional’n. Univ. “L’vivs’ka Politekhnika:” Fiz.-Mat. Nauky, Issue 660, 56–60 (2009).Google Scholar
- 9.Ya. M. Chabanyuk, “Approximation by diffusion process in averaging scheme,” Dopovidi NAN Ukrainy, Issue 12, 35–40 (2004).Google Scholar