Radonifying operators and infinitely divisible Wiener integrals

Markus Riedle

Department of Mathematics, King's College London, London WC2R 2LS, United Kingdom

Abstract: In this article we illustrate the relation between the existence of Wiener integrals with respect to a Lévy process in a separable Banach space and radonifying operators. For this purpose, we introduce the class of $\vartheta$-radonifying operators, i.e. operators which map a cylindrical measure $\vartheta$ to a genuine Radon measure. We study this class of operators for various examples of infinitely divisible cylindrical measures $\vartheta$ and highlight the differences from the Gaussian case.

Keywords: Cylindrical measures, infinitely divisible, stochastic integrals, reproducing kernel Hilbert space.

MSC: 60H05, 28C20, 47B32, 60E07

Language: English

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