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On Space-Time Regularity for the Stochastic Heat Equation on Lie Groups

✍ Scribed by Samy Tindel; Frederi Viens

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 312 KB
Volume: 169
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1999.3486

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✦ Synopsis

We consider the stochastic heat equations on Lie groups, that is, equations of the form t u=2 x u+b(u)+F(u) W 4 on R + _G, where G is a compact Lie group, 2 is the Laplace Beltrami operator on G, b and F are Lipschitz coefficients, and where W 4 is a Gaussian space-correlated noise, which is white-noise in time. We find necessary and sufficient conditions on the space correlation of W 4 such that u is an L 2 or Ho lder-continuous function in the spatial variable x, using some basic tools of stochastic analysis and harmonic analysis on the Lie group G.

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