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August 2017 An application of the KMT construction to the pathwise weak error in the Euler approximation of one-dimensional diffusion process with linear diffusion coefficient
Emmanuelle Clément, Arnaud Gloter
Ann. Appl. Probab. 27(4): 2419-2454 (August 2017). DOI: 10.1214/16-AAP1263

Abstract

It is well known that the strong error approximation in the space of continuous paths equipped with the supremum norm between a diffusion process, with smooth coefficients, and its Euler approximation with step 1/n is O(n1/2) and that the weak error estimation between the marginal laws at the terminal time T is O(n1). An analysis of the weak trajectorial error has been developed by Alfonsi, Jourdain and Kohatsu-Higa [Ann. Appl. Probab. 24 (2014) 1049–1080], through the study of the p-Wasserstein distance between the two processes. For a one-dimensional diffusion, they obtained an intermediate rate for the pathwise Wasserstein distance of order n2/3+ε. Using the Komlós, Major and Tusnády construction, we improve this bound assuming that the diffusion coefficient is linear and we obtain a rate of order logn/n.

Citation

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Emmanuelle Clément. Arnaud Gloter. "An application of the KMT construction to the pathwise weak error in the Euler approximation of one-dimensional diffusion process with linear diffusion coefficient." Ann. Appl. Probab. 27 (4) 2419 - 2454, August 2017. https://doi.org/10.1214/16-AAP1263

Information

Received: 1 June 2015; Revised: 1 November 2016; Published: August 2017
First available in Project Euclid: 30 August 2017

zbMATH: 06803467
MathSciNet: MR3693530
Digital Object Identifier: 10.1214/16-AAP1263

Subjects:
Primary: 60H35 , 65C30

Keywords: diffusion process , Euler scheme , quantile coupling technique , Wasserstein metric

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.27 • No. 4 • August 2017
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