Entrance and exit at infinity for stable jump diffusions

DOI10.1214/19-AOP1389zbMath1469.60211arXiv1802.01672WikidataQ114060548 ScholiaQ114060548MaRDI QIDQ784167

Andreas E. Kyprianou, Leif Döring

Publication date: 31 July 2020

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.01672

zbMATH Keywords

Kelvin transformdualitystable Lévy processesexplosionentranceSDEs

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Self-similar stochastic processes (60G18) Stable stochastic processes (60G52) Stochastic integral equations (60H20)

Related Items

Integral functionals for spectrally positive Lévy processes ⋮ Extinction time of logistic branching processes in a Brownian environment ⋮ On the entrance at infinity of Feller processes with no negative jumps ⋮ Time-changed spectrally positive Lévy processes started from infinity ⋮ Stable processes conditioned to hit an interval continuously from the outside ⋮ Stable Lévy processes in a cone ⋮ Convergence rates in uniform ergodicity by hitting times and \(L^2\)-exponential convergence rates ⋮ Dirichlet eigenvalues and exit time moments for symmetric Markov processes ⋮ Exponential and strong ergodicity for one-dimensional time-changed symmetric stable processes ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Deep factorisation of the stable process
• Perpetual integrals for Lévy processes
• Conditioning subordinators embedded in Markov processes
• Explicit identities for Lévy processes associated to symmetric stable processes
• Fluctuation theory and exit systems for positive self-similar Markov processes
• Time change equations for Lévy-type processes
• Markoff processes and potentials. I, II, III
• On Lévy processes conditioned to stay positive
• Duality theory for self-similar processes
• Semi-stable Markov processes in \(R^n\)
• On martingales and Feller semigroups
• On solutions of one-dimensional stochastic differential equations driven by stable Lévy motion
• Conditionings and path decompositions for Lévy processes
• The entrance laws of self-similar Markov processes and exponential functionals of Lévy processes
• Stable windings at the origin
• Conditioned real self-similar Markov processes
• On stochastic differential equations driven by a Cauchy process and other stable Lévy motions
• Real self-similar processes started from the origin
• \(\alpha\) -self-similar Markov processes
• A continuous-state polynomial branching process
• Fluctuations of Lévy processes with applications. Introductory lectures
• On Kelvin transformation
• The Lamperti representation of real-valued self-similar Markov processes
• Hitting distributions of \(\alpha\)-stable processes via path censoring and self-similarity
• The hitting time of zero for a stable process
• The Lamperti correspondence extended to Lévy processes and semi-stable Markov processes in locally compact groups
• Weak convergence of positive self-similar Markov processes and overshoots of Lévy processes
• Continuous additive functionals of a Markov process with applications to processes with independent increments
• Hitting times and potentials for recurrent stable processes
• The parabolic differential equations and the associated semigroups of transformation
• The general diffusion operator and positivity preserving semigroups in one dimension
• Stochastic-Process Limits
• Some applications of duality for Lévy processes in a half-line
• Some Useful Functions for Functional Limit Theorems
• Foundations of Modern Probability
• The Distribution of the First Hit for Stable and Asymptotically Stable Walks on an Interval
• Semi-stable Markov processes. I
• On the Harmonic Measure of Stable Processes
• Time Reversions of Markov Processes
• Markov processes and their functional in duality
• On the Distribution of First Hits for the Symmetric Stable Processes