Quasi-stationary distributions and Yaglom limits of self-similar Markov processes

DOI10.1016/j.spa.2012.08.006zbMath1267.60038arXiv1110.4795OpenAlexW2064236715MaRDI QIDQ713217

Bénédicte Haas, Víctor Manuel Rivero

Publication date: 26 October 2012

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.4795

zbMATH Keywords

Lévy processesextreme value theoryquasi-stationary distributionsself-similar Markov processesexponential functionals of Lévy processesYaglom limits

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Central limit and other weak theorems (60F05) Self-similar stochastic processes (60G18)

Related Items (18)

Spectral expansions of non-self-adjoint generalized Laguerre semigroups ⋮ Exponential functional of Lévy processes: generalized Weierstrass products and Wiener-Hopf factorization ⋮ Bernstein-gamma functions and exponential functionals of Lévy processes ⋮ Parisian quasi-stationary distributions for asymmetric Lévy processes ⋮ Ergodic aspects of some Ornstein-Uhlenbeck type processes related to Lévy processes ⋮ Exponentiality of first passage times of continuous time Markov chains ⋮ Self-similar solution for fractional Laplacian in cones ⋮ Implicit renewal theory for exponential functionals of Lévy processes ⋮ Yaglom limit for unimodal Lévy processes ⋮ Tail asymptotics for extinction times of self-similar fragmentations ⋮ On the density of exponential functionals of Lévy processes ⋮ Speed of convergence to the quasi-stationary distribution for Lévy input fluid queues ⋮ Yaglom limit for stochastic fluid models ⋮ Yaglom limit for stable processes in cones ⋮ Conditioning subordinators embedded in Markov processes ⋮ Conditional limit theorems for critical continuous-state branching processes ⋮ Probabilistic aspects of critical growth-fragmentation equations ⋮ On the Range of Exponential Functionals of Lévy Processes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Law of the absorption time of some positive self-similar Markov processes
• A refined factorization of the exponential law
• Asymptotic behavior of solutions of the fragmentation equation with shattering: an approach via self-similar Markov processes
• Exponential functionals of Lévy processes
• Lamperti-type laws
• Exponential functional of a new family of Lévy processes and self-similar continuous state branching processes with immigration
• The upper envelope of positive self-similar Markov Processes
• Residual life time at great age
• Statistical inference using extreme order statistics
• Itô excursion theory for self-similar Markov processes
• On the domain of attraction of \(\exp (-\exp (-x))\)
• Normalized excursion, meander and bridge for stable Lévy processes
• AIMD algorithms and exponential functionals
• Entrance from \(0+\) for increasing semi-stable Markov processes
• The entrance laws of self-similar Markov processes and exponential functionals of Lévy processes
• On subordinators, self-similar Markov processes and some factorizations of the exponential variable
• On the density of exponential functionals of Lévy processes
• Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct
• Recurrent extensions of self-similar Markov processes and Cramér's condition. II
• Recurrent extensions of self-similar Markov processes and Cramér's condition
• On powers of Stieltjes moment sequences, I
• Measure-valued Markov branching processes conditioned on non-extinction
• A Wiener-Hopf type factorization for the exponential functional of Lévy processes
• Entrance laws for positive self-similar Markov processes
• The Beta Product Distribution with Complex Parameters
• The Distribution of a Perpetuity, with Applications to Risk Theory and Pension Funding
• On certain self-decomposable distributions
• A law of iterated logarithm for increasing self-similar Markov processes
• Semi-stable Markov processes. I
• Conditioned stable Lévy processes and the Lamperti representation
• Random Fragmentation and Coagulation Processes
• Continuous-State Branching Processes and Self-Similarity
• A branching process with mean one and possibly infinite variance
• Maxima of sums of random variables and suprema of stable processes
• Spectral theory of semi-groups connected with diffusion processes and its application

This page was built for publication: Quasi-stationary distributions and Yaglom limits of self-similar Markov processes