【摘 要】
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Let Xt(x) be the solution of stochastic differential equations with smooth and bounded derivatives coefficients. Let Xnt (x) be the Euler discretization scheme
【机 构】
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School of Management,School of Mathematics and Statistics
论文部分内容阅读
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|6R|X nt (x,ω)-Xt (x,ω)|6ξR,γ(ω)2-nγ, n>1, q.e., whereξR,γ(ω) is quasi-everywhere finite.
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