On the Euler–Maruyama scheme for spectrally one-sided Lévy driven SDEs with Hölder continuous coefficients

Libo Li; Dai Taguchi

doi:10.1016/j.spl.2018.10.017

On the Euler–Maruyama scheme for spectrally one-sided Lévy driven SDEs with Hölder continuous coefficients

Libo Li, Dai Taguchi

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We study in this article the strong rate of convergence of the Euler–Maruyama scheme and associated with the jump-type equation introduced in Li and Mytnik (2011). We obtain the strong rate of convergence under similar assumptions for strong existence and pathwise uniqueness. Models of this type can be considered as a generalization of the CIR (Cox–Ingersoll–Ross) process with jumps.

Original language	English
Pages (from-to)	15-26
Number of pages	12
Journal	Statistics and Probability Letters
Volume	146
DOIs	https://doi.org/10.1016/j.spl.2018.10.017
Publication status	Published - Mar 2019
Externally published	Yes

Keywords

Euler–Maruyama scheme
Hölder continuous coefficients
Lévy driven SDEs
Spectrally positive Lévy process
α-CIR models

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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title = "On the Euler–Maruyama scheme for spectrally one-sided L{\'e}vy driven SDEs with H{\"o}lder continuous coefficients",

abstract = "We study in this article the strong rate of convergence of the Euler–Maruyama scheme and associated with the jump-type equation introduced in Li and Mytnik (2011). We obtain the strong rate of convergence under similar assumptions for strong existence and pathwise uniqueness. Models of this type can be considered as a generalization of the CIR (Cox–Ingersoll–Ross) process with jumps.",

keywords = "Euler–Maruyama scheme, H{\"o}lder continuous coefficients, L{\'e}vy driven SDEs, Spectrally positive L{\'e}vy process, α-CIR models",

author = "Libo Li and Dai Taguchi",

note = "Funding Information: The second author was supported by JSPS KAKENHI Grant Numbers 16J00894 and 17H06833 . ",

year = "2019",

month = mar,

doi = "10.1016/j.spl.2018.10.017",

language = "English",

volume = "146",

pages = "15--26",

journal = "Statistics and Probability Letters",

issn = "0167-7152",

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T1 - On the Euler–Maruyama scheme for spectrally one-sided Lévy driven SDEs with Hölder continuous coefficients

AU - Li, Libo

AU - Taguchi, Dai

N1 - Funding Information: The second author was supported by JSPS KAKENHI Grant Numbers 16J00894 and 17H06833 .

PY - 2019/3

Y1 - 2019/3

N2 - We study in this article the strong rate of convergence of the Euler–Maruyama scheme and associated with the jump-type equation introduced in Li and Mytnik (2011). We obtain the strong rate of convergence under similar assumptions for strong existence and pathwise uniqueness. Models of this type can be considered as a generalization of the CIR (Cox–Ingersoll–Ross) process with jumps.

AB - We study in this article the strong rate of convergence of the Euler–Maruyama scheme and associated with the jump-type equation introduced in Li and Mytnik (2011). We obtain the strong rate of convergence under similar assumptions for strong existence and pathwise uniqueness. Models of this type can be considered as a generalization of the CIR (Cox–Ingersoll–Ross) process with jumps.

KW - Euler–Maruyama scheme

KW - Hölder continuous coefficients

KW - Lévy driven SDEs

KW - Spectrally positive Lévy process

KW - α-CIR models

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DO - 10.1016/j.spl.2018.10.017

M3 - Article

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VL - 146

SP - 15

EP - 26

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

ER -

On the Euler–Maruyama scheme for spectrally one-sided Lévy driven SDEs with Hölder continuous coefficients

Abstract

Keywords

ASJC Scopus subject areas

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