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

ESAIM: Probability and Statistics (2012)

- 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 (2012): 110-138. <http://eudml.org/doc/222479>.

@article{Balan2012,

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 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.
},

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},

month = {1},

pages = {110-138},

publisher = {EDP Sciences},

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

url = {http://eudml.org/doc/222479},

volume = {15},

year = {2012},

}

TY - JOUR

AU - Balan, Raluca M.

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

JO - ESAIM: Probability and Statistics

DA - 2012/1//

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 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.

LA - eng

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

UR - http://eudml.org/doc/222479

ER -

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