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2019 Probability tilting of compensated fragmentations
Quan Shi, Alexander R. Watson
Electron. J. Probab. 24: 1-39 (2019). DOI: 10.1214/19-EJP316


Fragmentation processes are part of a broad class of models describing the evolution of a system of particles which split apart at random. These models are widely used in biology, materials science and nuclear physics, and their asymptotic behaviour at large times is interesting both mathematically and practically. The spine decomposition is a key tool in its study. In this work, we consider 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.


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Quan Shi. Alexander R. Watson. "Probability tilting of compensated fragmentations." Electron. J. Probab. 24 1 - 39, 2019.


Received: 25 June 2018; Accepted: 5 May 2019; Published: 2019
First available in Project Euclid: 6 August 2019

zbMATH: 07089016
MathSciNet: MR3991115
Digital Object Identifier: 10.1214/19-EJP316

Primary: 60G51, 60G55, 60J25, 60J80


Vol.24 • 2019
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