Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process

Aurélien Alfonsi

doi:10.1016/j.spl.2012.10.034

Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process

Aurélien Alfonsi

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi (2005) for the Cox-Ingersoll-Ross (CIR) process. Under general conditions, we obtain a strong convergence of order1. In the CIR case, Dereich etal. (2012) have shown recently a strong convergence of order1 / 2 for this scheme. Here, we obtain a strong convergence of order1 under more restrictive assumptions on the CIR parameters.

langue originale	Anglais
Pages (de - à)	602-607
Nombre de pages	6
journal	Statistics and Probability Letters
Volume	83
Numéro de publication	2
Les DOIs	https://doi.org/10.1016/j.spl.2012.10.034
état	Publié - 1 févr. 2013

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abstract = "We study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi (2005) for the Cox-Ingersoll-Ross (CIR) process. Under general conditions, we obtain a strong convergence of order1. In the CIR case, Dereich etal. (2012) have shown recently a strong convergence of order1 / 2 for this scheme. Here, we obtain a strong convergence of order1 under more restrictive assumptions on the CIR parameters.",

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N2 - We study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi (2005) for the Cox-Ingersoll-Ross (CIR) process. Under general conditions, we obtain a strong convergence of order1. In the CIR case, Dereich etal. (2012) have shown recently a strong convergence of order1 / 2 for this scheme. Here, we obtain a strong convergence of order1 under more restrictive assumptions on the CIR parameters.

AB - We study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi (2005) for the Cox-Ingersoll-Ross (CIR) process. Under general conditions, we obtain a strong convergence of order1. In the CIR case, Dereich etal. (2012) have shown recently a strong convergence of order1 / 2 for this scheme. Here, we obtain a strong convergence of order1 under more restrictive assumptions on the CIR parameters.

KW - Cox-Ingersoll-Ross model

KW - Drift implicit Euler scheme

KW - Lamperti transformation

KW - Strong error

UR - https://www.scopus.com/pages/publications/84870691951

U2 - 10.1016/j.spl.2012.10.034

DO - 10.1016/j.spl.2012.10.034

M3 - Article

AN - SCOPUS:84870691951

SN - 0167-7152

VL - 83

SP - 602

EP - 607

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 2

ER -

Strong order one convergence of a drift implicit Euler scheme: Application to the CIR process

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