Behavior of the Second Moment of the Solution to the Autonomous Stochastic Linear Partial Differential Equation with Random Parameters in the Right-Hand Side

Behavior of the Second Moment of the Solution to the Autonomous Stochastic Linear Partial Differential Equation with Random Parameters in the Right-Hand Side

The existence of a strong solution of the linear stochastic partial differential equation (LSPDE) in the corresponding space with random parameters is proved. The sufficient conditions are obtained for the asymptotic stability and mean square instability of the strong solution of the LSPDE.

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Veröffentlicht in:Cybernetics and systems analysis 2015-01, Vol.51 (1), p.56-63
Hauptverfasser: Koroliuk, V. S., Yurchenko, I. V., Yasynskyy, V. K.
Format: Artikel
Sprache:eng
Schlagworte:
Artificial Intelligence
Asymptotic methods
Bibliographic literature
Cauchy problems
Control
Cybernetics
Differential equations
Fourier transforms
Instability
Mathematical analysis
Mathematics
Mathematics and Statistics
Mean square values
Parameters
Partial differential equations
Processor Architectures
Random variables
Software Engineering/Programming and Operating Systems
Stability
Stochastic models
Stochasticity
Studies
Systems analysis
Systems stability
Systems Theory
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Beschreibung
Zusammenfassung:The existence of a strong solution of the linear stochastic partial differential equation (LSPDE) in the corresponding space with random parameters is proved. The sufficient conditions are obtained for the asymptotic stability and mean square instability of the strong solution of the LSPDE.
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-015-9697-x