Bernoulli

  • Bernoulli
  • Volume 17, Number 4 (2011), 1127-1135.

First passage time law for some Lévy processes with compound Poisson: Existence of a density

Laure Coutin and Diana Dorobantu

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Abstract

Let (Xt, t ≥ 0) be a Lévy process with compound Poisson process and τx be the first passage time of a fixed level x > 0 by (Xt, t ≥ 0). We prove that the law of τx has a density (defective when $\mathbb{E}(X_{1})\textless 0)$ with respect to the Lebesgue measure.

Article information

Source
Bernoulli Volume 17, Number 4 (2011), 1127-1135.

Dates
First available in Project Euclid: 4 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.bj/1320417498

Digital Object Identifier
doi:10.3150/10-BEJ323

Mathematical Reviews number (MathSciNet)
MR2854766

Keywords
first passage time law jump process Lévy process

Citation

Coutin, Laure; Dorobantu, Diana. First passage time law for some Lévy processes with compound Poisson: Existence of a density. Bernoulli 17 (2011), no. 4, 1127--1135. doi:10.3150/10-BEJ323. https://projecteuclid.org/euclid.bj/1320417498


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