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Stochastic fractional Anderson models with fractional noises. (English) Zbl 1185.35346
Summary: The authors are concerned with a class of one-dimensional stochastic Anderson models with double-parameter fractional noises, whose differential operators are fractional. A unique solution for the model in some appropriate Hilbert space is constructed. Moreover, the Lyapunov exponent of the solution is estimated, and its Hölder continuity is studied. On the other hand, the absolute continuity of the solution is also discussed.

MSC:
35R60 PDEs with randomness, stochastic partial differential equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R11 Fractional partial differential equations
35B65 Smoothness and regularity of solutions to PDEs
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