$L_p$-Theory for the Stochastic Heat Equation with Infinite-Dimensional Fractional Noise
| dc.creator | Balan, Raluca | |
| dc.date | 2009-05-13 | |
| dc.date.accessioned | 2026-07-07T13:14:33Z | |
| dc.date.available | 2026-07-07T13:14:33Z | |
| dc.description | In this article, we consider the stochastic heat equation $du=(Δu+f(t,x))dt+ \sum_{k=1}^{\infty} g^{k}(t,x) δβ_t^k, t \in [0,T]$, with random coefficients $f$ and $g^k$, driven by a sequence $(β^k)_k$ 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 $(β^k)_k$, we prove that the equation has a unique solution (in a Banach space of summability exponent $p \geq 2$), and this solution is Hölder continuous in both time and space. | |
| dc.identifier | https://arxiv.org/abs/0905.2150 | |
| dc.identifier | http://arxiv.org/abs/0905.2150 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230243 | |
| dc.subject | Probability | |
| dc.subject | 60H15; 60H07 | |
| dc.title | $L_p$-Theory for the Stochastic Heat Equation with Infinite-Dimensional Fractional Noise | |
| dc.type | text |