Infinitely divisible cylindrical measures on Banach spaces
Volume 207 / 2011
Studia Mathematica 207 (2011), 235-256 MSC: Primary 46G12; Secondary 46B09, 60B11, 60G20. DOI: 10.4064/sm207-3-2
In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a characterisation which is not known in general for infinitely divisible Radon measures on Banach spaces. Further properties of infinitely divisible cylindrical measures such as continuity are derived. Moreover, the classification result enables us to deduce new results on genuine Lévy measures on Banach spaces.