Stochastic heat equations driven by L\'evy processes

TL;DR

This paper investigates stochastic heat equations driven by Lévy processes, establishing estimates in Sobolev and Besov spaces that extend understanding of solutions under Lévy noise.

Contribution

It provides new a priori estimates for solutions of stochastic heat equations driven by Lévy processes in Sobolev and Besov spaces.

Findings

Established norm estimates for solutions in Sobolev spaces.

Extended analysis to Lévy process-driven stochastic heat equations.

Provided bounds depending on p, T, and function spaces.

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 $k \in \bR$.