TY - JOUR
T1 - Quasi-Sure Convergence Rate of Euler Scheme for Stochastic Differential Equations
AU - Huang, Wenliang
AU - Zhang, Xicheng
PY - 2014/1
Y1 - 2014/1
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 - http://www.scopus.com/inward/record.url?scp=84888806214&partnerID=8YFLogxK
U2 - 10.1016/S0252-9602(13)60126-5
DO - 10.1016/S0252-9602(13)60126-5
M3 - Article
AN - SCOPUS:84888806214
SN - 0252-9602
VL - 34
SP - 65
EP - 72
JO - Acta Mathematica Scientia
JF - Acta Mathematica Scientia
IS - 1
ER -