Stochastic analysis involving the Lévy Laplacian
The paper is a continuation of the investigation by the authors [C. R. Acad. Sci., Paris, Sér. I 320, No. 5, 597-602 (1995; Zbl 0832.60080)] of the Lévy-Ornstein-Uhlenbeck process, a stochastic process related to the Lévy Laplacian in a manner similar to the construction of the usual Ornstein-Uhlenbeck process in the finite-dimensional stochastic analysis. The authors define and study stochastic integrals, Sobolev classes and capacities associated with the Lévy-Ornstein-Uhlenbeck process. A version of the Malliavin calculus leads to the existence of a smooth density for a measure induced by a nondegenerate mapping of the Lévy-Wiener space.
scientific article; zbMATH DE number 1557260