Asymptotic Results for Heavy-tailed L\'evy Processes and their Exponential Functionals

@article{Xu2019AsymptoticRF,
  title={Asymptotic Results for Heavy-tailed L\'evy Processes and their Exponential Functionals},
  author={Wei Xu},
  journal={arXiv: Probability},
  year={2019}
}
  • W. Xu
  • Published 10 December 2019
  • Mathematics
  • arXiv: Probability
In this paper we first provide several conditional limit theorems for Levy processes with negative drift and regularly varying tail. Then we apply them to study the asymptotic behavior of expectations of some exponential functionals of heavy-tailed Levy processes. As the key point, we observe that the asymptotics mainly depends on the sample paths with early arrival large jump. Both the polynomial decay rate and the exact expression of the limit coefficients are given. As an application, we… 
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