Continuity of Certain Random Integral Mappings and the Uniform Integrability of Infinitely Divisible Measures

摘要

In this paper it is shown that the class of probability measures L(Q), which generalizes the classical Levy class L, is homeomorphic with the class ID sub log of all infinitely divisible probability measures having finite logarithmic moment. As an application of this result a set of generators of the entire class L(Q) is described. As a necessary tool, the relationship between the uniform integrability of infinitely divisible measures and of their corresponding Levy measures is studied and this may be of independent interest. (Author)