Parametric continuity of solutions to stochastic functional differential equations with poisson perturbations

The small-parameter method and the notion of averaged system are used to analyze the asymptotic stability in the mean square of the original system of stochastic differential equations. The stability of a system with continuous perturbations is considered. It is proved that the small-parameter metho...

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Bibliographic Details
Published in:Cybernetics and systems analysis 2012-11, Vol.48 (6), p.846-860
Main Authors: Yasinsky, V. K., Malyka, I. V.
Format: Article
Language:English
Subjects:
Artificial Intelligence
Asymptotic methods
Control
Control systems
Cybernetics
Differential equations
Discontinuity
Electron tubes
Euclidean space
Mathematics
Mathematics and Statistics
Perturbation methods
Poisson distribution
Processor Architectures
Radio communications
Software Engineering/Programming and Operating Systems
Stability
Stochastic models
Stochasticity
Studies
Systems analysis
Systems Theory
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Summary:The small-parameter method and the notion of averaged system are used to analyze the asymptotic stability in the mean square of the original system of stochastic differential equations. The stability of a system with continuous perturbations is considered. It is proved that the small-parameter method can be applied to stochastic differential equations with discontinuous trajectories, i.e., that stochastic differential depends on the Poisson integral.
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-012-9464-1