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.
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.
| Original language | English |
|---|---|
| Journal | Electronic Journal of Probability |
| Early online date | 6 Aug 2019 |
| DOIs | |
| Publication status | Published - 2019 |
Keywords
- Compensated fragmentation
- growth-fragmentation
- additive martingale
- derivative martingale
- spine decomposition
- many-to-one theorem