Volume 15, 2011
|Page(s)||110 - 138|
|Published online||05 January 2012|
Lp-theory for the stochastic heat equation with infinite-dimensional fractional noise*
University of Ottawa, Department of Mathematics and Statistics, 585 King Edward Avenue Ottawa, ON, K1N 6N5, Canada; firstname.lastname@example.org, http://aix1.uottawa.ca/~rbalan
Revised: 9 April 2009
In this article, we consider the stochastic heat equation , with random coefficients f and gk, driven by a sequence (βk)k of i.i.d. fractional Brownian motions of index H>1/2. Using the Malliavin calculus techniques and a p-th moment maximal inequality for the infinite sum of Skorohod integrals with respect to (βk)k, we prove that the equation has a unique solution (in a Banach space of summability exponent p ≥ 2), and this solution is Hölder continuous in both time and space.
Mathematics Subject Classification: 60H15 / 60H07
Key words: Fractional Brownian motion / Skorohod integral / maximal inequality / stochastic heat equation
© EDP Sciences, SMAI, 2011
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