# Lp-theory for the stochastic heat equation with infinite-dimensional fractional noise

ESAIM: Probability and Statistics (2011)

- Volume: 15, page 110-138
- ISSN: 1292-8100

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topBalan, Raluca M.. "Lp-theory for the stochastic heat equation with infinite-dimensional fractional noise." ESAIM: Probability and Statistics 15 (2011): 110-138. <http://eudml.org/doc/277158>.

@article{Balan2011,

abstract = {In this article, we consider the stochastic heat equation $du=(\Delta u+f(t,x))\{\rm d\}t+ \sum _\{k=1\}^\{\infty \} g^\{k\}(t,x) \delta \beta _t^k, t \in [0,T]$, with random coefficientsf 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.},

author = {Balan, Raluca M.},

journal = {ESAIM: Probability and Statistics},

keywords = {fractional brownian motion; Skorohod integral; maximal inequality; stochastic heat equation; fractional Brownian motion},

language = {eng},

pages = {110-138},

publisher = {EDP-Sciences},

title = {Lp-theory for the stochastic heat equation with infinite-dimensional fractional noise},

url = {http://eudml.org/doc/277158},

volume = {15},

year = {2011},

}

TY - JOUR

AU - Balan, Raluca M.

TI - Lp-theory for the stochastic heat equation with infinite-dimensional fractional noise

JO - ESAIM: Probability and Statistics

PY - 2011

PB - EDP-Sciences

VL - 15

SP - 110

EP - 138

AB - In this article, we consider the stochastic heat equation $du=(\Delta u+f(t,x)){\rm d}t+ \sum _{k=1}^{\infty } g^{k}(t,x) \delta \beta _t^k, t \in [0,T]$, with random coefficientsf 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.

LA - eng

KW - fractional brownian motion; Skorohod integral; maximal inequality; stochastic heat equation; fractional Brownian motion

UR - http://eudml.org/doc/277158

ER -

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