The Annals of Applied Probability

Ergodic approximation of the distribution of a stationary diffusion: Rate of convergence

Gilles Pagès and Fabien Panloup

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Abstract

We extend to Lipschitz continuous functionals either of the true paths or of the Euler scheme with decreasing step of a wide class of Brownian ergodic diffusions, the central limit theorems formally established for their marginal empirical measure of these processes (which is classical for the diffusions and more recent as concerns their discretization schemes). We illustrate our results by simulations in connection with barrier option pricing.

Article information

Source
Ann. Appl. Probab. Volume 22, Number 3 (2012), 1059-1100.

Dates
First available in Project Euclid: 18 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1337347539

Digital Object Identifier
doi:10.1214/11-AAP779

Mathematical Reviews number (MathSciNet)
MR2977986

Zentralblatt MATH identifier
1252.60080

Subjects
Primary: 60G10: Stationary processes 60J60: Diffusion processes [See also 58J65] 65C05: Monte Carlo methods 65D15: Algorithms for functional approximation 60F05: Central limit and other weak theorems

Keywords
Stochastic differential equation stationary process steady regime ergodic diffusion central limit theorem Euler scheme

Citation

Pagès, Gilles; Panloup, Fabien. Ergodic approximation of the distribution of a stationary diffusion: Rate of convergence. Ann. Appl. Probab. 22 (2012), no. 3, 1059--1100. doi:10.1214/11-AAP779. https://projecteuclid.org/euclid.aoap/1337347539.


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