Invariant measures under random integral mappings and marginal   distributions of fractional L\'evy processes
  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 $(\star)$ 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 L\'evy process (MAFLP). 
Zbigniew J. Jurek
math.PR