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

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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.