Differential Equations with Small Stochastic Terms Under the Lévy Approximating Conditions

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...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2018-02, Vol.69 (9), p.1445-1454
Main Authors: Samoilenko, I. V., Nikitin, A.V.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Approximation
Catastrophic events
Differential equations
Geometry
Markov chains
Mathematics
Mathematics and Statistics
Statistics
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Summary: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.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-018-1443-x