On subclasses of infinitely divisible distributions on R related to hitting time distributions of 1-dimensional generalized diffusion processes

Abstract

A distribution μ on R+ = [0, ∞) is said to be a distribution if there are an increasing (in the strict sense) sequence of positive real numbers such that, for each j = 0, …, m, there is at least one ak satisfying bj < ak < b+1 and theLaplace transform of μ is represented as