A stochastic Fubini theorem for α-stable process

Huiyan Zhao and Siyan Xu

Statistics & Probability Letters, 2020, vol. 160, issue C

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.

Keywords: Stochastic Fubini theorem; α-stable Lévy process; Mild solution; Weak solution (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108700

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