A stochastic Fubini theorem for α-stable process

Publication date: Available online 18 January 2020Source: Statistics & Probability LettersAuthor(s): Huiyan Zhao, Siyan XuAbstractIn 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.

Source: Statistics and Probability Letters - January 19, 2020 Category: Statistics Source Type: research