Quasi-invariance properties of a class of subordinators

TL;DR

This paper investigates the quasi-invariance of certain stochastic processes, including gamma and Dirichlet processes, demonstrating local equivalence of their laws under non-linear transformations and deriving explicit Radon-Nikodym densities.

Contribution

It generalizes previous results by establishing quasi-invariance properties for a broad class of processes and transformations, with explicit density computations.

Findings

Laws of non-linear transformations are locally equivalent to original processes.

Explicit Radon-Nikodym densities are derived for these transformations.

The results unify and extend prior quasi-invariance findings for gamma and Dirichlet processes.

Abstract

We study absolute-continuity properties of a class of stochastic processes, including the gamma and the Dirichlet processes. We prove that the laws of a general class of non-linear transformations of such processes are locally equivalent to the law of the original process and we compute explicitly the associated Radon-Nikodym densities. This work unifies and generalizes to random non-linear transformations several previous results on quasi-invariance of gamma and Dirichlet processes.