Sample Paths of the Solution to the Fractional-colored Stochastic Heat Equation

Abstract

Let u = {u(t, x), t $\in$ [0, T ], x $\in$ R d } be the solution to the linear stochastic heat equation driven by a fractional noise in time with correlated spatial structure. We study various path properties of the process u with respect to the time and space variable, respectively. In particular, we derive their exact uniform and local moduli of continuity and Chung-type laws of the iterated logarithm.

References in corpus (1)

• Fractal properties of the random string processes

Cited by in corpus (1)

• Smoothness of Local Times and Self-Intersection Local Times of Gaussian Random Fields