Stochastic heat equations driven by L\'evy processes

Abstract

We study stochastic heat equations driven by a class of L\'evy processes: du = \De u dt + g dX_t \quad in \quad \bR^d_T, \qquad u(0,x)= 0 \quad in \quad x \in \bR^d. We prove the corresponding estimate \[\norm{u}_{\bH_p^k(\RT)} \le c(p,T) \norm{g}_{\bB_p^{k-\frac2p}(\RT)}\] for $2\le p<\infty$ and $k \in \bR$.