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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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.

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

First available in Project Euclid: 18 May 2012

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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

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


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.

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