Optimal Approximation Rate of Certain Stochastic Integrals
نویسنده
چکیده
Given an increasing function H : [0, 1) → [0,∞) and An(H) := inf τ∈Tn n X i=1 Z ti ti−1 (ti − t)H (t)dt ! 1 2 , where Tn := {τ = (ti) n i=0 : 0 = t0 < t1 < · · · < tn = 1}, we characterize the property An(H) ≤ c √ n , and give conditions for An(H) ≤ c √ nβ and An(H) ≥ 1 c √ nβ for β ∈ (0, 1), both in terms of integrability properties of H . These results are applied to the approximation of certain stochastic integrals.
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تاریخ انتشار 2009