Invariant measures under random integral mappings and marginal distributions of fractional L\'evy processes

摘要

It is shown that some convolution semigroups of infinitely divisible measuresare invariant under the random integral mappings $I^{h,r}_{(a,b]}$ defined in$(\star)$ below. The converse implication is specified for the semigroups ofgeneralized s-selfdecomposable and selfdecomposable distributions. Someapplication are given to the moving average fractional L\'evy process (MAFLP).