The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional brownian motion
By Tomás Caraballo, María J. Garrido-Atienza, Takeshi Taniguchi. 2011
324 citations recorded by the source corpus.
Abstract 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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/74501aaef96dd6c394758de3781905d803e93b6f
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In Applied Mathematics
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Citations in the corpus
- The existence and Hyers-Ulam stability of solution for almost periodical fractional stochastic differential equation with fBm (2020, unknown): “2), then, for any a, b 2 1⁄20,T with a> b (see [60])”
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- Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains (2013, background): “Since then, such attractors for autonomous stochastic PDEs have been studied in [6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 30, 31] in bounded domains, and in [4, 33, 34] in unbounded domains.”
- Existence and Upper Semicontinuity of Attractors for Stochastic Equations with Deterministic Non-autonomous Terms (2012, background): “rbations and can be considered as a parametric space. The existence of random attractors for systems over a single probability space has been investigated by many experts in the literature, see e.g., [1, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 20, 21, 22, 26, 27, 32, 35] and the references therein. Th”
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