The present book offers a detailed treatment of perturbed random walks, perpetuities, and
random processes with immigration. These objects are of major importance in modern …

We consider a family of random trees satisfying a Markov branching property. Roughly, this
property says that the subtrees above some given height are independent with a law that …

We study how memory impacts passages at the origin for a so-called elephant random walk
in the diffusive regime. We observe that the number of zeros always grows asymptotically …

We are interested in the asymptotic behavior of Markov chains on the set of positive integers
for which, loosely speaking, large jumps are rare and occur at a rate that behaves like a …

Consider a stochastic process that behaves as a d-dimensional simple and symmetric
random walk, except that, with a certain fixed probability, at each step, it chooses instead to …

The class of coalescent processes with simultaneous multiple collisions (Ξ-coalescents)
without proper frequencies is considered. We study the asymptotic behavior of the external …

The Mittag-Leffler process $ X=(X_t) _ {t\ge 0} $ is introduced. This Markov process has the
property that its marginal random variables $ X_t $ are Mittag-Leffler distributed with …

We provide exact large-time equivalents of the density and upper tail distributions of the
exponential functional of a subordinator in terms of its Laplace exponents. This improves …

Representation of coalescent process using pruning of trees has been used by Goldschmidt
and Martin for the Bolthausen-Sznitman coalescent and by Abraham and Delmas for the …

Kingman's theory of partition structures relates, via a natural sampling procedure, finite
partitions to hypothetical infinite populations. Explicit formulas for distributions of such …