Probability tilting of compensated fragmentations

Q. Shi, A. R. Watson

Abstract

Fragmentation processes are part of a broad class of models describing the evolution of a system of particles which split apart at random. Their asymptotic behaviour at large times is of crucial interest, and the spine decomposition is a key tool in its study. In this work, we study the class of compensated fragmentations, or homogeneous growth-fragmentations, recently defined by Bertoin. We give a complete spine decomposition of these processes in terms of a Lévy process with immigration, and apply our result to study the asymptotic properties of the derivative martingale.

Type
article
Publication
Electronic Journal of Probability, 24, no. 78, 1–39
Date
August 2019
Links
DOI Preprint