QUASI-SURE CONVERGENCE RATE OF EULER SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS

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

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (1): 65-72.doi: 10.1016/S0252-9602(13)60126-5

QUASI-SURE CONVERGENCE RATE OF EULER SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS

黄文亮|张希承

School of Management, Shanghai University of Science and Technology, Shanghai 200093, China|Department of Mathematic, East China University of Science and Technology, Shanghai 200237, China|School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2012-10-30 出版日期:2014-01-20 发布日期:2014-01-20

QUASI-SURE CONVERGENCE RATE OF EULER SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS

HUANG Wen-Liang, ZHANG Xi-Cheng

School of Management, Shanghai University of Science and Technology, Shanghai 200093, China|Department of Mathematic, East China University of Science and Technology, Shanghai 200237, China|School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2012-10-30 Online:2014-01-20 Published:2014-01-20

摘要/Abstract

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),
sup_{t∈[0,1],|x|≤R}|Xⁿ_t(x, ω) − X_t(x, ω)| ξ _R, γ(ω)2^−nγ, n > 1, q.e.,
where ξ_{R, γ}(ω) is quasi-everywhere finite.

关键词: Euler approximation, quasi-sure convergence, SDE

Abstract:

Key words: Euler approximation, quasi-sure convergence, SDE

中图分类号:

60H15

黄文亮, 张希承. QUASI-SURE CONVERGENCE RATE OF EULER SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2014, 34(1): 65-72.

HUANG Wen-Liang, ZHANG Xi-Cheng. QUASI-SURE CONVERGENCE RATE OF EULER SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS[J]. Acta mathematica scientia,Series B, 2014, 34(1): 65-72.

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QUASI-SURE CONVERGENCE RATE OF EULER SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS

QUASI-SURE CONVERGENCE RATE OF EULER SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS

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