Bernoulli

  • Bernoulli
  • Volume 23, Number 3 (2017), 1631-1662.

First time to exit of a continuous Itô process: General moment estimates and ${\mathrm{L}}_{1}$-convergence rate for discrete time approximations

Bruno Bouchard, Stefan Geiss, and Emmanuel Gobet

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Abstract

We establish general moment estimates for the discrete and continuous exit times of a general Itô process in terms of the distance to the boundary. These estimates serve as intermediate steps to obtain strong convergence results for the approximation of a continuous exit time by a discrete counterpart, computed on a grid. In particular, we prove that the discrete exit time of the Euler scheme of a diffusion converges in the ${\mathbf{L}}_{1}$ norm with an order $1/2$ with respect to the mesh size. This rate is optimal.

Article information

Source
Bernoulli, Volume 23, Number 3 (2017), 1631-1662.

Dates
Received: September 2014
Revised: October 2015
First available in Project Euclid: 17 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.bj/1489737620

Digital Object Identifier
doi:10.3150/15-BEJ791

Mathematical Reviews number (MathSciNet)
MR3624873

Zentralblatt MATH identifier
06714314

Keywords
Euler scheme exit time strong approximation

Citation

Bouchard, Bruno; Geiss, Stefan; Gobet, Emmanuel. First time to exit of a continuous Itô process: General moment estimates and ${\mathrm{L}}_{1}$-convergence rate for discrete time approximations. Bernoulli 23 (2017), no. 3, 1631--1662. doi:10.3150/15-BEJ791. https://projecteuclid.org/euclid.bj/1489737620


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