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.
Mots-clés : fractional brownian motion, Skorohod integral, maximal inequality, stochastic heat equation
@article{PS_2011__15__110_0,
author = {Balan, Raluca M.},
title = {$L_p$-theory for the stochastic heat equation with infinite-dimensional fractional noise},
journal = {ESAIM: Probability and Statistics},
pages = {110--138},
publisher = {EDP-Sciences},
volume = {15},
year = {2011},
doi = {10.1051/ps/2009006},
zbl = {1263.60054},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ps/2009006/}
}
TY - JOUR AU - Balan, Raluca M. TI - $L_p$-theory for the stochastic heat equation with infinite-dimensional fractional noise JO - ESAIM: Probability and Statistics PY - 2011 SP - 110 EP - 138 VL - 15 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2009006/ DO - 10.1051/ps/2009006 LA - en ID - PS_2011__15__110_0 ER -
%0 Journal Article %A Balan, Raluca M. %T $L_p$-theory for the stochastic heat equation with infinite-dimensional fractional noise %J ESAIM: Probability and Statistics %D 2011 %P 110-138 %V 15 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2009006/ %R 10.1051/ps/2009006 %G en %F PS_2011__15__110_0
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. http://www.numdam.org/articles/10.1051/ps/2009006/
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