Random distributions, random affine systems, sampling of renewal processes

Abstract

Let F be a neutral to the right, random distribution function on [0,+∞[, with a stationary subordinator. We introduce new linear functionals of the increments of F. Each of them is distributed like the unique fixed point of a random affine system. For gamma subordinators, we prove, building on earlier work, that their densities involve linear combinations of hypergeometric functions. We apply these ideas to the random sampling of alternating renewal processes.