# 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} }

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

#### One Citation

Precise asymptotics for the density and the upper tail of exponential functionals of subordinators

- Mathematics
- 2021

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 results… Expand

#### 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 determine… Expand

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 and… Expand

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 q… Expand

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 by… Expand

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-valued… Expand

Law of the absorption time of some positive self-similar Markov processes

- Mathematics
- 2012

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 an… Expand

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 us… Expand

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 method… Expand

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 existence… Expand