Acta mathematica scientia, Series B >
QUASI-SURE CONVERGENCE RATE OF EULER SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS
Received date: 2012-10-30
Online published: 2014-01-20
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|Xnt (x, ω) − Xt(x, ω)| ξ R, γ(ω)2−nγ, n > 1, q.e.,
where ξR, γ(ω) is quasi-everywhere finite.
Key words： Euler approximation; quasi-sure convergence; SDE
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 . DOI: 10.1016/S0252-9602(13)60126-5
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