Hölder continuity for stochastic fractional heat equation with colored noise

Kexue Li

Statistics & Probability Letters, 2017, vol. 129, issue C, 34-41

Abstract: In this paper, we consider semilinear stochastic fractional heat equation ∂ut∂t=−(−△)β/2ut+σ(ut)η̇. The Gaussian noise η̇ is assumed to be colored in space with covariance of the form E(η̇(t,x)η̇(s,y))=δ0(t−s)fα(x−y), where fα is the Riesz kernel fα(x)∝∣x∣−α. We obtain the spatial and temporal Hölder continuity of the mild solution.

Keywords: Stochastic fractional heat equation; Fractional heat kernel; Colored noise; Hölder continuity (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.04.020

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