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• W2894026062 abstract "In this paper, we study the following stochastic heat equation [ partial_tu=mathcal{L} u(t,x)+dot{B},quad u(0,x)=0,quad 0le tle T,quad xinmathbb{R}d, ] where $mathcal{L}$ is the generator of a L'evy process $X$ taking value in $mathbb{R}^d$, $B$ is a fractional-colored Gaussian noise with Hurst index $Hinleft(frac12,,1right)$ for the time variable and spatial covariance function $f$ which is the Fourier transform of a tempered measure $mu.$ After establishing the existence of solution for the stochastic heat equation, we study the regularity of the solution ${u(t,x),, tge 0,, xinmathbb{R}^d}$ in both time and space variables. Under mild conditions, we give the exact uniform modulus of continuity and a Chung-type law of iterated logarithm for the sample function $(t,x)mapsto u(t,x)$. Our results generalize and strengthen the corresponding results of Balan and Tudor (2008) and Tudor and Xiao (2017)." @default.
• W2894026062 created "2018-10-05" @default.
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• W2894026062 date "2018-09-28" @default.
• W2894026062 modified "2023-09-25" @default.
• W2894026062 title "Sharp Space-Time Regularity of the Solution to Stochastic Heat Equation Driven by Fractional-Colored Noise" @default.
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• W2894026062 doi "https://doi.org/10.48550/arxiv.1810.00066" @default.
• W2894026062 hasPublicationYear "2018" @default.
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