On the class of distributions of subordinated L\'evy processes

TL;DR

This paper investigates the distributions resulting from subordinating Lévy processes and bases, deriving properties of a Lévy mixing mapping to address the recovery problem for these processes.

Contribution

It introduces new properties of a Lévy mixing mapping and applies them to solve the recovery problem for subordinated Lévy processes and bases.

Findings

Derived properties of Lévy mixing mapping.

Solved the recovery problem for Lévy bases.

Applicable to moving average processes driven by subordinated Lévy processes.

Abstract

This article study the class of distributions obtained by subordinating L\'evy processes and L\'evy bases. To do this we derive properties of a suitable mapping obtained via L\'evy mixing. We show that our results can be used to solve the so-called recovery problem for general L\'evy bases as well as for moving average processes which are driven by subordinated L\'evy processes.