Differential equations with small stochastic supplements under Poisson approximation conditions / Samoilenko, / Chabanyuk, / Nikitin, / Himka. (2017)
Ukrainian

English  Cybernetics and Systems Analysis   /     Issue (2017, 53 (3))

Samoilenko I.V., Chabanyuk Y.M., Nikitin A.V., Himka U.T.
Differential equations with small stochastic supplements under Poisson approximation conditions

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. © 2017, Springer Science+Business Media New York.

Keywords: generator on Banach space, Markov process, Poisson approximation, stochastic approximation procedure, stochastic diffusion equation, Approximation theory, Banach spaces, Differential equations, Markov processes, Poisson distribution, Poisson equation, Stochastic systems, Approximation scheme, Asymptotic behaviors, Evolutionary system, Poisson approximations, Stochastic approximations, Stochastic diffusion, Stochastic evolution, System disturbances, Stochastic models


Cite:
Samoilenko I.V., Chabanyuk Y.M., Nikitin A.V., Himka U.T. (2017). Differential equations with small stochastic supplements under Poisson approximation conditions. Cybernetics and Systems Analysis, 53 (3), 93-99. doi: https://doi.org/10.1007/s10559-017-9941-7 http://jnas.nbuv.gov.ua/article/UJRN-0000700162 [In Russian].


 

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