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arXiv · 1501.06828

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

Ciprian A. Tudor·Yimin Xiao
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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.

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Ciprian A. Tudor, Yimin Xiao. 2015-01-27. Sample Paths of the Solution to the Fractional-colored Stochastic Heat Equation. https://arxiv.org/abs/1501.06828

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