Randomly shifted lattice rules for unbounded integrands
نویسندگان
چکیده
منابع مشابه
Randomly shifted lattice rules for unbounded integrands
We study the problem of multivariate integration over Rd with integrands of the form f(x)ρ(x) where ρ is a probability density function. Our study is motivated by problems in mathematical finance, where unbounded integrands over [0, 1]d can arise as a result of using transformations to map the integral to the unit cube. We assume that the functions f belong to some weighted Hilbert space. We ca...
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We study the problem of multivariate integration on the unit cube for unbounded integrands. Our study is motivated by problems in statistics and mathematical finance, where unbounded integrands can arise as a result of using the cumulative inverse normal transformation to map the integral from the unbounded domain Rd to the unit cube [0, 1]d. We define a new space of functions which possesses t...
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We study the convergence of the variance for randomly shifted lattice rules for numerical multiple integration over the unit hypercube in an arbitrary number of dimensions. We consider integrands that are square integrable but whose Fourier series are not necessarily absolutely convergent. For such integrands, a bound on the variance is expressed through a certain type of weighted discrepancy. ...
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We examine the question of constructing shifted lattice rules of rank one with an arbitrary number of points n, an arbitrary shift, and small weighted star discrepancy. An upper bound on the weighted star discrepancy, that depends on the lattice parameters and is easily computable, serves as a figure of merit. It is known that there are lattice rules for which this upper bound converges as O(n−...
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2006
ISSN: 0885-064X
DOI: 10.1016/j.jco.2006.04.006