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On a class of stochastic Anderson models with fractional noises. (English) Zbl 1136.60345
Summary: We are concerned with a class of one-dimensional fourth order stochastic Anderson models with double-parameter fractional noises with Hurst parameter \(H = (h_1, h_2)\in (\frac 1 2 , 1)\times (\frac 1 2 , 1)\). The unique solution is constructed for the model in some appropriate Hilbert space. On the other hand, we shall estimate the Lyapunov exponent of the solution and study its regularity.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
34A34 Nonlinear ordinary differential equations and systems, general theory
49N60 Regularity of solutions in optimal control
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