Radonifying operators and infinitely divisible Wiener integrals

2015/06/16 by Markus Riedle, Riedle, Markus
Economics, Econometrics and Finance · Mathematics · #Mathematical Analysis and Transform Methods #Stochastic processes and financial applications #advanced mathematical theories #math.PR #msc:28C20 #msc:47B32 #msc:60E07 #msc:60H05

paper · pdf · doi:10.48550/arxiv.1506.05142

16 pages

arxiv created 2015/06/16 · arxiv updated 2015/06/18

Abstract

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

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