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August 2020 Edgeworth expansion for Euler approximation of continuous diffusion processes
Mark Podolskij, Bezirgen Veliyev, Nakahiro Yoshida
Ann. Appl. Probab. 30(4): 1971-2003 (August 2020). DOI: 10.1214/19-AAP1549

Abstract

In this paper we present the Edgeworth expansion for the Euler approximation scheme of a continuous diffusion process driven by a Brownian motion. Our methodology is based upon a recent work (Stochastic Process. Appl. 123 (2013) 887–933), which establishes Edgeworth expansions associated with asymptotic mixed normality using elements of Malliavin calculus. Potential applications of our theoretical results include higher order expansions for weak and strong approximation errors associated to the Euler scheme, and for studentized version of the error process.

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Mark Podolskij. Bezirgen Veliyev. Nakahiro Yoshida. "Edgeworth expansion for Euler approximation of continuous diffusion processes." Ann. Appl. Probab. 30 (4) 1971 - 2003, August 2020. https://doi.org/10.1214/19-AAP1549

Information

Received: 1 November 2018; Revised: 1 September 2019; Published: August 2020
First available in Project Euclid: 4 August 2020

MathSciNet: MR4132642
Digital Object Identifier: 10.1214/19-AAP1549

Subjects:
Primary: 60F05, 60H10, 65C30

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 4 • August 2020
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