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Stochastic delay evolution equations driven by sub-fractional Brownian motion. (English) Zbl 1343.60086
Summary: In this paper, we investigate the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a sub-fractional Brownian motion \(S^{H}_{Q}(t)\): \(dX(t)=(AX(t)+f(t,X_{t}))\, dt+g(t)\, dS^{H}_{Q}(t)\) with index \(H\in(1/2,1)\).

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60G15 Gaussian processes
60H05 Stochastic integrals
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