Optimal importance sampling for the approximation of integrals
نویسندگان
چکیده
منابع مشابه
Optimal sampling design for approximation of stochastic Itô integrals with application to the nonlinear Lebesgue integration
where T > 0 is a given number, a function f : [0, T ]× R → R satisfies certain regularity conditions and (Bt)t∈[0,T ] is a one dimensional Brownian motion on some probability space (Ω,Σ,P). Since in most cases explicit value of the integral (1) is not available, we must consider approximation schemes. We are interested in algorithms which use only discrete values of the driving Brownian motion ...
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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 cert...
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2010
ISSN: 0885-064X
DOI: 10.1016/j.jco.2009.11.003