On a Class of Stochastic Anderson Models with Fractional Noises

Abstract

In this article, we are concerned with a class of one-dimensional fourth order stochastic Anderson models with double-parameter fractional noises with Hurst parameter . 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.

Keywords:

• Fourth order Anderson models
• Fractional noises
• Lyapunov exponent
• Regularity

Mathematics Subject Classification:

• Primary 60H15
• Secondary 34A34, 49N60

This work is supported partially by the LPMC at Nankai University and the NSF of China (No. 10471003). The authors would like to thank the referee for his suggestions to improve the article.