Invariant measures under random integral mappings and marginal distributions of fractional Lévy processes

Abstract

It is shown that some convolution semigroups of infinitely divisible measures are invariant under the random integral mappings I h,r (a,b] defined in (⋆) below. The converse implication is specified for the semigroups of generalized s-selfdecomposable and selfdecomposable distributions. Some application are given to the moving average fractional Lévy process (MAFLP). (2000): Primary 60F05 , 60E07, 60B11; Secondary 60H05, 60B10. Mathematics Subject Classifications