Isotropic self-similar Markov processes

TL;DR

This paper characterizes when isotropic self-similar Markov processes in Euclidean space can be decomposed into independent radial and angular components, based on their jump behaviors.

Contribution

It establishes a necessary and sufficient condition for the skew product structure in such processes, linking it to the simultaneous jumps of radial and angular parts.

Findings

Skew product structure exists if radial and angular parts do not jump simultaneously.

The paper provides a clear criterion for the independence of radial and angular components.

It advances understanding of the structure of isotropic self-similar Markov processes.

Abstract

We show that an isotropic self-similar Markov process in ${\Bbb R}^d$ has a skew product structure if and only if its radial and angular parts do not jump at the same time.