文献类型：期刊文献

中文题名：QUASI-SURE CONVERGENCE RATE OF EULER SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS

英文题名：QUASI-SURE CONVERGENCE RATE OF EULER SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS

作者：Huang, Wenliang[1,2];Zhang, Xicheng[3]

机构：[1]Shanghai Univ Sci & Technol, Sch Management, Shanghai 200093, Peoples R China;[2]E China Univ Sci & Technol, Dept Mathemat, Shanghai 200237, Peoples R China;[3]Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

年份：2014

卷号：34

期号：1

起止页码：65

中文期刊名：Acta Mathematica Scientia

外文期刊名：ACTA MATHEMATICA SCIENTIA

收录：CSTPCD;;Scopus;WOS:【SCI-EXPANDED(收录号:WOS:000330090300004)】；CSCD:【CSCD2013_2014】；

语种：英文

中文关键词：Euler approximation; quasi-sure convergence; SDE

外文关键词：Euler approximation; quasi-sure convergence; SDE

摘要：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）, sup t∈[0,1],｜x｜≤R｜X nt （x,ω）-Xt （x,ω）｜≤ξR,γ（ω）2-nγ, n≥1, q.e., whereξR,γ（ω） is quasi-everywhere finite.
Let X-t (x) be the solution of stochastic differential equations with smooth and bounded derivatives coefficients. Let X-t(n)(x) be the Euler discretization scheme of SDEs with step 2(-n). In this note, we prove that for any R> 0 and gamma epsilon (0,1/2), sup vertical bar X-t(n)(x,w) - X-t(x,w)vertical bar <= xi R,gamma(w)2-n gamma, n >= 1, q.e., t epsilon[0,1],vertical bar x vertical bar <= R where xi R,gamma(w) is quasi-everywhere finite.