Electronic Journal of Probability

Probability tilting of compensated fragmentations

Quan Shi and Alexander R. Watson

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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

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

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

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Zentralblatt MATH identifier

Primary: 60G51: Processes with independent increments; Lévy processes 60J25: Continuous-time Markov processes on general state spaces 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60G55: Point processes

compensated fragmentation growth-fragmentation additive martingale derivative martingale spine decomposition many-to-one theorem

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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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