H\xf6lder estimates of mild solutions for nonlocal SPDEs

Abstract

We consider nonlocal PDEs driven by additive white noises on {mathbb{R}}^{d}. For L^{q} integrable coefficients, we derive the existence and uniqueness, as well as Hölder continuity, of mild solutions. Precisely speaking, the unique mild solution is almost surely Hölder continuous with Hölder index 0<theta <(1/2-d/(q alpha))(1wedge alpha). Moreover, we show that any order gamma (< q) moment of Hölder normal for u on every bounded domain of {mathbb{R}}_{+}times {mathbb{R}}^{d} is finite.