## Electronic Journal of Probability

### Probability tilting of compensated fragmentations

#### Abstract

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.

#### Article information

Source
Electron. J. Probab., Volume 24 (2019), paper no. 78, 39 pp.

Dates
Accepted: 5 May 2019
First available in Project Euclid: 6 August 2019

https://projecteuclid.org/euclid.ejp/1565057003

Digital Object Identifier
doi:10.1214/19-EJP316

Mathematical Reviews number (MathSciNet)
MR3991115

Zentralblatt MATH identifier
07089016

#### Citation

Shi, Quan; Watson, Alexander R. Probability tilting of compensated fragmentations. Electron. J. Probab. 24 (2019), paper no. 78, 39 pp. doi:10.1214/19-EJP316. https://projecteuclid.org/euclid.ejp/1565057003

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