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Edgeworth expansion for Euler approximation of continuous diffusion processes

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Edgeworth expansion for Euler approximation of continuous diffusion processes. / Podolskij, Mark; Veliyev, Bezirgen; Yoshida, Nakahiro.

In: Annals of Applied Probability, Vol. 30, No. 4, 2020, p. 1971-2003.

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Podolskij, Mark ; Veliyev, Bezirgen ; Yoshida, Nakahiro. / Edgeworth expansion for Euler approximation of continuous diffusion processes. In: Annals of Applied Probability. 2020 ; Vol. 30, No. 4. pp. 1971-2003.

Bibtex

@article{3544e002bdee44d383806e2d24a49a6e,
title = "Edgeworth expansion for Euler approximation of continuous diffusion processes",
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 [22], 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.",
author = "Mark Podolskij and Bezirgen Veliyev and Nakahiro Yoshida",
year = "2020",
doi = "10.1214/19-AAP1549",
language = "English",
volume = "30",
pages = "1971--2003",
journal = "Annals of Applied Probability",
issn = "1050-5164",
publisher = "Institute of Mathematical Statistics",
number = "4",

}

RIS

TY - JOUR

T1 - Edgeworth expansion for Euler approximation of continuous diffusion processes

AU - Podolskij, Mark

AU - Veliyev, Bezirgen

AU - Yoshida, Nakahiro

PY - 2020

Y1 - 2020

N2 - 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 [22], 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.

AB - 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 [22], 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.

U2 - 10.1214/19-AAP1549

DO - 10.1214/19-AAP1549

M3 - Journal article

VL - 30

SP - 1971

EP - 2003

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 4

ER -