Precise asymptotics for the density and the upper tail of exponential functionals of subordinators
arXiv:2106.08691
Abstract
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 on the logarithmic asymptotic behaviour of the upper tail. Since the results in their general form remain rather abstract, we study some fairly common situations in details to see how the behavior near 0 of the Lévy measure of the subordinator influences the asymptotics of the density and upper tail distributions. Several examples of applications are then discussed.
References in corpus (4)
- Recurrent extensions of self-similar Markov processes and Cramér's condition II
- On the distribution of exponential functionals for Levy processes with jumps of rational transform
- Self-similar scaling limits of non-increasing Markov chains
- Asymptotic behavior of solutions of the fragmentation equation with shattering: An approach via self-similar Markov processes