Corpus ID: 233210047

# Asymptotic of densities of exponential functionals of subordinators

@inproceedings{Minchev2021AsymptoticOD,
title={Asymptotic of densities of exponential functionals of subordinators},
author={M. Minchev and M. Savov},
year={2021}
}
• Published 2021
• Mathematics
In this paper we derive non-classical Tauberian asymptotic at infinity for the tail, the density and the derivatives thereof of a large class of exponential functionals of subordinators. More precisely, we consider the case when the Lévy measure of the subordinator satisfies the wellknown and mild condition of positive increase. This is achieved via a convoluted application of the saddle point method to the Mellin transform of these exponential functionals which is given in terms of Bernstein… Expand
1 Citations
Precise asymptotics for the density and the upper tail of exponential functionals of subordinators
We provide exact large-time equivalents of the density and upper tail distributions of the exponential functional of a subordinator in terms of its Laplace exponents. This improves previous resultsExpand

#### References

SHOWING 1-10 OF 40 REFERENCES
Bivariate Bernstein–gamma functions and moments of exponential functionals of subordinators
• Mathematics
• 2019
In this paper, we extend recent work on the functions that we call Bernstein-gamma to the class of bivariate Bernstein-gamma functions. In the more general bivariate setting, we determineExpand
Fluctuations of Stable Processes and Exponential Functionals of Hypergeometric Lévy Processes
• Mathematics
• 2010
We study the distribution and various properties of exponential functionals of hypergeometric Lévy processes. We derive an explicit formula for the Mellin transform of the exponential functional andExpand
On the density of exponential functionals of Lévy processes
• Mathematics
• 2011
In this paper, we study the existence of the density associated to the exponential functional of the Levy process ξ, Ieq := ∫ eq 0 es ds, where eq is an independent exponential r.v. with parameter qExpand
Extended Factorizations of Exponential Functionals of Lévy Processes
• Mathematics
• 2011
Pardo, Patie, and Savov derived , under mild conditions, a Wiener - Hopf type factorization for the exponential functional of proper L evy processes. In this paper, we extend this factorization byExpand
A Wiener-Hopf type factorization for the exponential functional of Lévy processes
• Mathematics, Computer Science
• J. Lond. Math. Soc.
• 2012
This work uses and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual MarkOV process. Expand
Spectral expansions of non-self-adjoint generalized Laguerre semigroups
• Mathematics
• 2015
We provide the spectral expansion in a weighted Hilbert space of a substantial class of invariant non-self-adjoint and non-local Markov operators which appear in limit theorems for positive-valuedExpand
Law of the absorption time of some positive self-similar Markov processes
Let X be a spectrally negative self-similar Markov process with 0 as an absorbing state. In this paper, we show that the distribution of the absorption time is absolutely continuous with anExpand
On exponential functionals, harmonic potential measures and undershoots of subordinators
• Mathematics
• 2013
We establish a link between the distribution of an exponential functional I and the undershoots of a subordinator, which is given in terms of the associated harmonic potential measure. This allows usExpand
Bernstein-gamma functions and exponential functionals of Levy Processes
• Mathematics
• 2016
We study the equation $M_\Psi(z+1)=\frac{-z}{\Psi(-z)}M_\Psi(z), M_\Psi(1)=1$ defined on a subset of the imaginary line and where $\Psi$ is a negative definite functions. Using the Wiener-Hopf methodExpand
Quasi-stationary distributions and Yaglom limits of self-similar Markov processes
• Mathematics
• 2011
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 the existenceExpand