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The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional Brownian motion. (English) Zbl 1218.60053
Summary: We investigate the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic delay evolution equations perturbed by a fractional Brownian motion \(B^H_Q(t)\),
\[ dX(t)=(AX(t)+f(t,X_t))\,dt+g(t)\,dB^H_Q(t), \]
with Hurst parameter \(H\in (1/2,1)\). We also consider the existence of weak solutions.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60G22 Fractional processes, including fractional Brownian motion
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