Approximation for non-smooth functionals of stochastic differential equations with irregular drift

Hoang Long Ngo; Dai Taguchi

doi:10.1016/j.jmaa.2017.08.006

Approximation for non-smooth functionals of stochastic differential equations with irregular drift

Hoang Long Ngo, Dai Taguchi

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

4 Citations (Scopus)

Abstract

This paper aims at developing a systematic study for the weak rate of convergence of the Euler–Maruyama scheme for stochastic differential equations with very irregular drift and constant diffusion coefficients. We apply our method to obtain the rates of approximation for the expectation of various non-smooth functionals of both stochastic differential equations and killed diffusion. We also apply our method to the study of the weak approximation of reflected stochastic differential equations whose drift is Hölder continuous.

Original language	English
Pages (from-to)	361-388
Number of pages	28
Journal	Journal of Mathematical Analysis and Applications
Volume	457
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2017.08.006
Publication status	Published - Jan 1 2018
Externally published	Yes

Keywords

Euler–Maruyama approximation
Irregular drift
Monte Carlo method
Reflected stochastic differential equation
Weak approximation

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2017.08.006

Cite this

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title = "Approximation for non-smooth functionals of stochastic differential equations with irregular drift",

abstract = "This paper aims at developing a systematic study for the weak rate of convergence of the Euler–Maruyama scheme for stochastic differential equations with very irregular drift and constant diffusion coefficients. We apply our method to obtain the rates of approximation for the expectation of various non-smooth functionals of both stochastic differential equations and killed diffusion. We also apply our method to the study of the weak approximation of reflected stochastic differential equations whose drift is H{\"o}lder continuous.",

keywords = "Euler–Maruyama approximation, Irregular drift, Monte Carlo method, Reflected stochastic differential equation, Weak approximation",

author = "Ngo, {Hoang Long} and Dai Taguchi",

note = "Funding Information: This work was completed while H.N. was staying at Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the institute for support. This work was also partly supported by the Vietnamese National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.03-2014.14 . D.T. was supported by JSPS KAKENHI Grant Number 16J00894 . Both authors thank Arturo Kohatsu-Higa and an anonymous referee for their helpful comments and suggestions which have improved the readability of this paper. Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

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doi = "10.1016/j.jmaa.2017.08.006",

language = "English",

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AU - Ngo, Hoang Long

AU - Taguchi, Dai

N1 - Funding Information: This work was completed while H.N. was staying at Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the institute for support. This work was also partly supported by the Vietnamese National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.03-2014.14 . D.T. was supported by JSPS KAKENHI Grant Number 16J00894 . Both authors thank Arturo Kohatsu-Higa and an anonymous referee for their helpful comments and suggestions which have improved the readability of this paper. Publisher Copyright: © 2017 Elsevier Inc.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - This paper aims at developing a systematic study for the weak rate of convergence of the Euler–Maruyama scheme for stochastic differential equations with very irregular drift and constant diffusion coefficients. We apply our method to obtain the rates of approximation for the expectation of various non-smooth functionals of both stochastic differential equations and killed diffusion. We also apply our method to the study of the weak approximation of reflected stochastic differential equations whose drift is Hölder continuous.

AB - This paper aims at developing a systematic study for the weak rate of convergence of the Euler–Maruyama scheme for stochastic differential equations with very irregular drift and constant diffusion coefficients. We apply our method to obtain the rates of approximation for the expectation of various non-smooth functionals of both stochastic differential equations and killed diffusion. We also apply our method to the study of the weak approximation of reflected stochastic differential equations whose drift is Hölder continuous.

KW - Euler–Maruyama approximation

KW - Irregular drift

KW - Monte Carlo method

KW - Reflected stochastic differential equation

KW - Weak approximation

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VL - 457

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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ER -

Approximation for non-smooth functionals of stochastic differential equations with irregular drift

Abstract

Keywords

ASJC Scopus subject areas

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