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Stochastic fractional Anderson models with fractional noises

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

    Yiming Jiang, Kehua Shi & Yongjin Wang

Authors
  1. Yiming Jiang
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  2. Kehua Shi
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  3. Yongjin Wang
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Correspondence to Yiming Jiang.

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Projects supported by the National Natural Science Foundation of China (No. 10871103).

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Jiang, Y., Shi, K. & Wang, Y. Stochastic fractional Anderson models with fractional noises. Chin. Ann. Math. Ser. B 31, 101–118 (2010). https://doi.org/10.1007/s11401-008-0244-1

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  • DOI: https://doi.org/10.1007/s11401-008-0244-1

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