On additive time-changes of Feller processes

TL;DR

This paper extends Phillips' theorem to include additive subordinators, allowing for nonstationary increments, and provides explicit characteristics of the subordinated process when starting from a Levy process.

Contribution

It generalizes the subordination of Feller processes to additive subordinators and derives explicit characteristics for the resulting process.

Findings

Generalization of Phillips' theorem to additive subordinators

Explicit characterization of subordinated process with Levy starting point

Applicable to nonstationary increment processes

Abstract

In this note we generalise the Phillips theorem on the subordination of Feller processes by Levy subordinators to the class of additive subordinators (i.e. subordinators with independent but possibly nonstationary increments). In the case where the original Feller process is Levy we also express the time-dependent characteristics of the subordinated process in terms of the characteristics of the Levy process and the additive subordinator.