Moment Generating Functions of Random Variables and Asymptotic Behaviour for Generalized Feller Operators

Abstract

After giving the representation of moment generating function for the $S$-$\u03bb$ type random variable by solving a differential equation, we prove that this type random variable is of regular $n$-$r$ order moment. Furthermore, we establish the higher order asymptotic formula for generalized Feller operators by making use of the generalized Taylor formula.