Inhomogeneous Levy processes in Lie groups and homogeneous spaces

TL;DR

This paper generalizes the Levy-Ito representation to inhomogeneous Levy processes in Lie groups and homogeneous spaces without assuming stochastic continuity, broadening the scope of stochastic process representations.

Contribution

It provides a new representation of inhomogeneous Levy processes in Lie groups and homogeneous spaces, relaxing the assumption of stochastic continuity.

Findings

Representation in terms of drift, matrix, and measure functions

Generalization of Levy-Ito representation to non-stochastically continuous processes

Extension from Euclidean spaces to Lie groups and homogeneous spaces

Abstract

We obtain a representation of an inhomogeneous Levy process in a Lie group or a homogeneous space in terms of a drift, a matrix function and a measure function. Because the stochastic continuity is not assumed, our result generalizes the well known Levy-Ito representation for stochastic continuous processes with independent increments in Euclidean spaces and the extension to Lie groups.