The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion

In this paper we investigate the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a fractional Brownian motion B Q H ( t ) : d X ( t ) = ( A X ( t ) + f ( t , X t ) ) d t + g ( t ) d B Q H ( t ) , with Hurst parameter H...

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Bibliographic Details
Published in:Nonlinear analysis 2011-07, Vol.74 (11), p.3671-3684
Main Authors: Caraballo, T., Garrido-Atienza, M.J., Taniguchi, T.
Format: Article
Language:English
Subjects:
Asymptotic properties
Brownian motion
Delay
Delay stochastic PDEs
Evolution
Exact sciences and technology
Exponential decay in mean square
Fractional Brownian motion
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
Stochasticity
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Uniqueness
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Summary:In this paper we investigate the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a fractional Brownian motion B Q H ( t ) : d X ( t ) = ( A X ( t ) + f ( t , X t ) ) d t + g ( t ) d B Q H ( t ) , with Hurst parameter H ∈ ( 1 / 2 , 1 ) . We also consider the existence of weak solutions.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2011.02.047