Quasi-Sure Convergence Rate of Euler Scheme for Stochastic Differential Equations

Wenliang Huang; Xicheng Zhang

doi:10.1016/S0252-9602(13)60126-5

Quasi-Sure Convergence Rate of Euler Scheme for Stochastic Differential Equations

Wenliang Huang^*
, Xicheng Zhang

^*此作品的通讯作者

University of Shanghai for Science and Technology
East China University of Science and Technology
Wuhan University

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

Let X_t(x) be the solution of stochastic differential equations with smooth and bounded derivatives coefficients. Let Xⁿ_t(x) be the Euler discretization scheme of SDEs with step 2^-n. In this note, we prove that for any R > 0 and γ ∈ (0,1/2), supt∈[0,1],|x|≤R|Xtn(x,ω)-Xt(x,ω)|≤ξR,γ(ω)2 nγ,n≥1,q.e.,where ξR,γ(ω) is quasi-everywhere finite.

源语言	英语
页（从-至）	65-72
页数	8
期刊	Acta Mathematica Scientia
卷	34
期	1
DOI	https://doi.org/10.1016/S0252-9602(13)60126-5
出版状态	已出版 - 1月 2014
已对外发布	是

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title = "Quasi-Sure Convergence Rate of Euler Scheme for Stochastic Differential Equations",

abstract = "Let Xt(x) be the solution of stochastic differential equations with smooth and bounded derivatives coefficients. Let Xnt(x) be the Euler discretization scheme of SDEs with step 2-n. In this note, we prove that for any R > 0 and γ ∈ (0,1/2), supt∈[0,1],|x|≤R|Xtn(x,ω)-Xt(x,ω)|≤ξR,γ(ω)2 nγ,n≥1,q.e.,where ξR,γ(ω) is quasi-everywhere finite.",

keywords = "Euler approximation, Quasi-sure convergence, SDE",

author = "Wenliang Huang and Xicheng Zhang",

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AU - Zhang, Xicheng

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N2 - Let Xt(x) be the solution of stochastic differential equations with smooth and bounded derivatives coefficients. Let Xnt(x) be the Euler discretization scheme of SDEs with step 2-n. In this note, we prove that for any R > 0 and γ ∈ (0,1/2), supt∈[0,1],|x|≤R|Xtn(x,ω)-Xt(x,ω)|≤ξR,γ(ω)2 nγ,n≥1,q.e.,where ξR,γ(ω) is quasi-everywhere finite.

AB - Let Xt(x) be the solution of stochastic differential equations with smooth and bounded derivatives coefficients. Let Xnt(x) be the Euler discretization scheme of SDEs with step 2-n. In this note, we prove that for any R > 0 and γ ∈ (0,1/2), supt∈[0,1],|x|≤R|Xtn(x,ω)-Xt(x,ω)|≤ξR,γ(ω)2 nγ,n≥1,q.e.,where ξR,γ(ω) is quasi-everywhere finite.

KW - Euler approximation

KW - Quasi-sure convergence

KW - SDE

UR - https://www.scopus.com/pages/publications/84888806214

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EP - 72

JO - Acta Mathematica Scientia

JF - Acta Mathematica Scientia

IS - 1

ER -

Quasi-Sure Convergence Rate of Euler Scheme for Stochastic Differential Equations

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