| Issue |
ESAIM: PS
Volume 15, 2011
|
|
|---|---|---|
| Page(s) | 110 - 138 | |
| DOI | https://doi.org/10.1051/ps/2009006 | |
| 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; rbalan@uottawa.ca, http://aix1.uottawa.ca/~rbalan
Received:
15
January
2009
Revised:
9
April
2009
In this article, we consider the stochastic heat equation ![$du=(\Delta u+f(t,x)){\rm d}t+ \sum_{k=1}^{\infty} g^{k}(t,x) \delta \beta_t^k, t \in [0,T]$](/articles/ps/abs/2011/01/ps0901/ps0901_tex_eq2.png)
, 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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