Compositions of mappings of infinitely divisible distributions with applications to finding the limits of some nested subclasses

Abstract

Let $\{X_t^{(\mu)},t\ge 0\}$ be a L\'evy process on $R^d$ whose distribution at time 1 is $\mu$, and let $f$ be a nonrandom measurable function on $$ for such general $f$'s are investigated by using the idea of compositions of suitable mappings of infinitely divisible distributions.