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In this article, we propose a class of high-order stochastic partial differential equations (SPDEs) for spatial dimensions d < 5 which might be called high-order stochastic Anderson models. This class of the equations is perturbed by a space-time white noise when d < 3 and by a space-correlated Gaussian noise when d = 4, 5. The objectives of this article are to get some estimates on the Lyapunov exponent of the solutions and to study the convergence rates of the chaos expansions of the solutions for the models.

Lyapunov exponent estimates of a class of higher-order stochastic Anderson models