A Markov Additive Process is a bi-variate Markov process $(\xi, J)=\big ((\xi_t, J_t),
t\geq0\big) $ which should be thought of as a multi-type L\'evy process: the second …

We encode a certain class of stochastic fragmentation processes, namely self-similar
fragmentation processes with a negative index of self-similarity, into a metric family tree …

We study a natural fragmentation process of the so-called stable tree introduced by
Duquesne and Le Gall, which consists in removing the nodes of the tree according to a …

We show that the genealogy of any self-similar fragmentation process can be encoded in a
compact measured real tree. Under some Malthusian hypotheses, we compute the fractal …

Markovian growth-fragmentation processes describe a family of particles which can grow
larger or smaller with time, and occasionally split in a conservative manner. They were …

The fragmentation processes considered in this work are self-similar Markov processes
which are meant to describe the evolution of a mass that falls apart randomly as time …

The purpose of the present work is twofold. First, we develop the theory of general self-
similar growth-fragmentation processes by focusing on martingales which appear naturally …

Similarly as in (Electron. J. Probab. 23 (2018)) where nested coalescent processes are
studied, we generalize the definition of partition-valued homogeneous Markov fragmentation …

Some, but not all processes of the form M_t=\exp(-t) for a pure-jump subordinator ξ with
Laplace exponent Φ arise as residual mass processes of particle 1 (tagged particle) in …

In this paper, we study Ruelle's probability cascades in the framework of time-
inhomogeneous fragmentation processes. We describe Ruelle's cascades mechanism …