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

Ciprian A. Tudor (1) , Yimin Xiao (2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 Department of Mathematics and Statistics

Let u = {u(t, x), t ∈ [0, T ], x ∈ 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.

Mots clés: law of the iterated logarithm; fractional Brownian motion; Stochastic heat equation; Gaussian noise; path regularity

Domaines: Probabilités [math.PR]

Ciprian A. Tudor, Yimin Xiao. Sample Paths of the Solution to the Fractional-colored Stochastic Heat Equation. 2015. ⟨hal-01108721v2⟩