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.
| Original language | English |
|---|---|
| Pages (from-to) | 1-42 |
| Number of pages | 42 |
| Journal | Stochastic Processes and their Applications |
| Volume | 165 |
| DOIs | |
| Publication status | Published - Nov 2023 |
Keywords
- Domain of attraction
- Exponential functional
- Random walk
- Regular variation
- Spitzer's condition
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Xu, W. (2023). Asymptotics for exponential functionals of random walks. Stochastic Processes and their Applications, 165, 1-42. https://doi.org/10.1016/j.spa.2023.07.013