A stochastic Fubini theorem for [formula omitted]-stable process

Abstract

In this paper, we give an elementary proof of a stochastic Fubini theorem, which says that one can interchange a Lebesgue integral and a stochastic integral with respect to an α-stable (1<α<2) Lévy process. As an application, the equivalence between weak and mild solutions for a class of semi-linear SPDEs with α-stable (1<α<2) noise is established.