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Probability tilting of compensated fragmentations

Shi, Q; Watson, AR; (2019) Probability tilting of compensated fragmentations. Electronic Journal of Probability , 24 , Article 78. 10.1214/19-EJP316. Green open access

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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.

Type: Article
Title: Probability tilting of compensated fragmentations
Open access status: An open access version is available from UCL Discovery
DOI: 10.1214/19-EJP316
Publisher version: https://doi.org/10.1214/19-EJP316
Language: English
Additional information: This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/10079232
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