On tails of exit times of multidimensional L\'evy processes

Rafał Marcin Łochowski

On tails of exit times of multidimensional L\'evy processes

Probability 2018-11-07 v2

Authors: Rafał Marcin Łochowski

Abstract

Using a very simple argument based on the indepenence of increments and the fact that in a finite dimensional space $R^{d}$ there are not too many directions, we derive a theorem stating that exit time of any (non-constant) L\'{e}vy process on $R^{d}$ from a ball has exponentially light tails.

Keywords

Lévy processes exit times exponential tails multidimensional independent increments

Cite

@article{arxiv.1809.06037,
  title  = {On tails of exit times of multidimensional L\'evy processes},
  author = {Rafał Marcin Łochowski},
  journal= {arXiv preprint arXiv:1809.06037},
  year   = {2018}
}

Comments

Estimates with better constants may be obtained from the estimate in Proposition 5.2 in: "Asymptotic Behaviour and Estimates of Slowly Varying Convolution Semigroups" by Tomasz Grzywny, Micha{\l} Ryznar and Bartosz Trojan

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