Hölder Continuity for the Stochastic Heat Equation With Spatially Correlated Noise
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We study the Hölder continuity in time and space of the solution of a stochastic heat equation with spatial parameter of any dimension d and spatially correlated noise. The conditions for this property to hold are given first in terms of the spectral measure of the noise and then by means of the correlation measure.
Keywords and phrasesStochastic partial differential equations Hölder continuity heat equation
2000 Mathematics Subject ClassificationPrimary 60H15 60H05 Secondary 35K90
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