Geodesic
L p -theory for the stochastic heat equation with infinite-dimensional fractional noise
ESAIM: Probability and Statistics, Tome 15 (2011), pp. 110-138

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In this article, we consider the stochastic heat equation du=(Δu+f(t,x))dt+∑ k=1 ∞ g k (t,x)δβ t k ,t∈[0,T], 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.

DOI : 10.1051/ps/2009006
Classification : 60H15, 60H07
Keywords: fractional brownian motion, Skorohod integral, maximal inequality, stochastic heat equation 
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     title = {$L_p$-theory for the stochastic heat equation with infinite-dimensional fractional noise},
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     pages = {110--138},
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     year = {2011},
     doi = {10.1051/ps/2009006},
     zbl = {1263.60054},
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Balan, Raluca M. $L_p$-theory for the stochastic heat equation with infinite-dimensional fractional noise. ESAIM: Probability and Statistics, Tome 15 (2011), pp. 110-138. doi: 10.1051/ps/2009006

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