It is shown that some convolution semigroups of infinitely divisible measures are invariant under certain random integral mappings. We characterize the coincidence of random integrals for s-selfdecomposable and selfdecomposable distributions. Some applications are given to the moving average...

Upsilon transformations satisfying certain regularity conditions are shown to generate semigroups of such transformations. This is based on a general commutativity property of the Upsilon transformations, and uses log infinite divisibility. The existence of random integral representations of...