A refined factorization of the exponential law

DOI10.3150/10-BEJ292zbMath1253.60020arXiv1005.4011MaRDI QIDQ453305

Pierre Patie

Publication date: 19 September 2012

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.4011

zbMATH Keywords

Lévy processessubordinatorexponential functionalself-similar Markov processself-decomposable random variableStieltjes moment sequences

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Continuous-time Markov processes on general state spaces (60J25) Self-similar stochastic processes (60G18)

Related Items

Spectral expansions of non-self-adjoint generalized Laguerre semigroups ⋮ On the self-decomposability of the Fréchet distribution ⋮ On the unimodality of power transformations of positive stable densities ⋮ Weak similarity orbit of (log)‐self‐similar Markov semigroups on the Euclidean space ⋮ On temporally completely monotone functions for Markov processes ⋮ On non-local ergodic Jacobi semigroups: spectral theory, convergence-to-equilibrium and contractivity ⋮ Quasi-stationary distributions and Yaglom limits of self-similar Markov processes ⋮ Intertwining, excursion theory and Krein theory of strings for non-self-adjoint Markov semigroups ⋮ Extinction time of non-Markovian self-similar processes, persistence, annihilation of jumps and the Fréchet distribution ⋮ On Doney's striking factorization of the arc-sine law ⋮ A transformation for spectrally negative Lévy processes and applications ⋮ Gibbs partitions, Riemann–Liouville fractional operators, Mittag–Leffler functions, and fragmentations derived from stable subordinators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Implicit renewal theory and tails of solutions of random equations
• On powers of Stieltjes moment sequences. II
• Exponential functionals of Lévy processes
• Exponential functional of a new family of Lévy processes and self-similar continuous state branching processes with immigration
• Special, conjugate and complete scale functions for spectrally negative Lévy processes
• Random difference equations and renewal theory for products of random matrices
• On the entire moments of self-similar Markov processes and exponential functionals of Lévy 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
• A transformation from Hausdorff to Stieltjes moment sequences
• Weak convergence of positive self-similar Markov processes and overshoots of Lévy processes
• Introductory lectures on fluctuations of Lévy processes with applications.
• Recurrent extensions of self-similar Markov processes and Cramér's condition
• On powers of Stieltjes moment sequences, I
• q-Invariant Functions for Some Generalizations of the Ornstein-Uhlenbeck Semigroup
• A law of iterated logarithm for increasing self-similar Markov processes
• Sur les fonctionnelles exponentielles de certains processus de lévy
• Semi-stable Markov processes. I
• Exponential functionals of Brownian motion and related processes