7 papers · 1 filter
Asymptotics for Beta-Splitting Trees via Homogeneous Fragmentations and Meromorphic Potential Theory
Yoana R. Chorbadzhiyska, Martin Minchev, Mladen Savov
Inspired by recent work of Aldous, Janson, and Pittel on the critical beta-splitting model, we study the full beta-splitting family for beta greater than minus two through a canoni…
On a moment determinacy conjecture of Bertoin and Yor
Martin Minchev
Let be an unkilled real-valued Lévy process which drifts to and has positive exponential moments of all orders, and define , and it…
Recent developments in exponential functionals of Lévy processes
Martin Minchev, Mladen Savov
This survey aims to review two decades of progress on exponential functionals of (possibly killed) real-valued Lévy processes. Since the publication of the seminal survey by Berto…
Preferential relocations enhance survival for Markov chains with killing
Jean Bertoin, Martin Minchev
We investigate the impact on survival of a modification of the evolution of a sub-stochastic Markov chain that involves random relocations at previously visited states. Our central…
Multi-type branching processes with immigration generated by point processes
Martin Minchev, Maroussia Slavtchova-Bojkova
Following the pivotal work of Sevastyanov, who considered branching processes with homogeneous Poisson immigration, much has been done to understand the behaviour of such processes…
Bivariate Bernstein-gamma functions, potential measures, and asymptotics of exponential functionals of Lévy processes
Martin Minchev, Mladen Savov
Let be a Lévy process and , be the exponential functional of Lévy processes on deterministic horizon. Given that $\lim_{…