Asymptotics for Exponential Functionals of Random Walks
Probability
2025-04-29 v3
Abstract
This paper provides a detailed description for the asymptotics of exponential functionals of random walks with light/heavy tails. We give the convergence rate based on the key observation that the asymptotics depends on the sample paths with either slowly decreasing local minimum or final value below a low level. Also, our thoughtful analysis of the interrelationship between the local minimum and the final value provides the exact expression for the limiting coefficients in terms of some transformations of the random walk.
Cite
@article{arxiv.2201.02975,
title = {Asymptotics for Exponential Functionals of Random Walks},
author = {Wei Xu},
journal= {arXiv preprint arXiv:2201.02975},
year = {2025}
}
Comments
43 pages, 1 Figure, 1 table. We thank Zhihao Cui and Hao Wu a lot for pointing out several typos and errors that have been highlightened with red color