| Volume 7, Number 2, 2017, Pages 581-599 DOI：10.11948/2017036 |
| On $L_p$-solution of fractional heat equation driven by fractional Brownian motion |
| Litan Yan,Xianye Yu |
| Keywords:Fractional Brownian motion, fractional heat equation, the Littlewood-Paley inequality. |
| Abstract: |
| In this paper, we study the fractional stochastic heat equation driven by fractional Brownian motions of the form
$$
du(t,x)=\left(-(-\Delta)^{\alpha/2}u(t,x)+f(t,x)\right)dt +\sum\limits^{\infty}_{k=1} g^k(t,x)\delta\beta^k_t
$$
with $u(0,x)=u_0$, $t\in[0,T]$ and $x\in\mathbb{R}^d$, where $\beta^k=\{\beta^k_t,t\in[0,T]\},k\geq1$ is a sequence of i.i.d. fractional Brownian motions with the same Hurst index $H>1/2$ and the integral with respect to fractional Brownian motion is Skorohod integral. By adopting the framework given by Krylov, we prove the existence and uniqueness of $L_p$-solution to such equation. |
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