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 …

In this work we analyse the solution to the recurrence equation M_Ψ(z+1)=-zΨ(-
z)M_Ψ(z),\quadM_Ψ(1)=1, defined on a subset of the imaginary line and where -Ψ is any …

Stable Lévy processes lie at the intersection of Lévy processes and self-similar Markov
processes. Processes in the latter class enjoy a Lamperti-type representation as the space …

Asymptotics for densities of exponential functionals of subordinators Page 1 Bernoulli 29(4),
2023, 3307–3333 https://doi.org/10.3150/23-BEJ1584 Asymptotics for densities of exponential …

We discuss the existence and characterization of quasi-stationary distributions and Yaglom
limits of self-similar Markov processes that reach 0 in finite time. By Yaglom limit, we mean …

Let $\xi=(\xi_t, t\ge 0) $ be a real-valued L\'evy process and define its associated exponential
functional as follows\[I_t (\xi):=\int_0^ t\exp\{-\xi_s\}{\rm d} s,\qquad t\ge 0.\] Motivated by …

We study the distribution of the exponential functional $ I (\xi,\eta)=\int_0^{\infty}\exp (\xi_ {t-})
d\eta_t $, where $\xi $ and $\eta $ are independent Lévy processes. In the general setting …

In 18, under mild conditions, a Wiener-Hopf type factorization is derived for the exponential
functional of proper Lévy processes. In this paper, we extend this factorization by relaxing a …

Markovian growth-fragmentation processes introduced in [8, 9] extend the pure-
fragmentation model by allowing the fragments to grow larger or smaller between …

We investigate the effects of noise reinforcement on a Bessel process of dimension d∈(0,
2), and more specifically on the asymptotic behavior of its additive functionals. This leads us …