排序方式: 共有13条查询结果,搜索用时 15 毫秒
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Zoltán Buczolich Gunther Leobacher Alexander Steinicke 《Mathematische Nachrichten》2023,296(10):4778-4805
We construct a Hölder continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We conclude that this function has impermeable graph—one of the key concepts introduced in this paper—and we present further examples of functions both with permeable and impermeable graphs. Moreover, we show that typical (in the sense of Baire category) continuous functions have permeable graphs. The first example function is subsequently used to construct an example of a continuous function on the plane which is intrinsically Lipschitz continuous on the complement of the graph of a Hölder continuous function with impermeable graph, but which is not Lipschitz continuous on the plane. As another main result, we construct a continuous function on the unit interval which coincides in a set of Hausdorff dimension 1 with every function of total variation smaller than 1 which passes through the origin. 相似文献
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Gunther Leobacher 《Mathematical Methods of Operations Research》2008,67(1):65-90
This paper generalizes earlier work by G. Larcher and the author about hedging with short-term futures contracts, a problem
which was considered in connection with the debacle of the German company Metallgesellschaft. While the original problem corresponded
to the simplest possible model for the price process, i.e. Brownian motion, we give here solutions to more general models,
i.e. a mean reverting model (Ornstein–Uhlenbeck process) and geometric Brownian motion. Furthermore we allow for interest
rates greater than 0. 相似文献
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We use so-called (t, α, d)-sequences and Smolyak's algorithm to construct d × l -dimensional integration rules with optimal convergence rates in a suitable function space. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Ligia L. Cristea Josef Dick Gunther Leobacher Friedrich Pillichshammer 《Numerische Mathematik》2007,105(3):413-455
In this paper we investigate multivariate integration in reproducing kernel Sobolev spaces for which the second partial derivatives
are square integrable. As quadrature points for our quasi-Monte Carlo algorithm we use digital (t,m,s)-nets over which are randomly digitally shifted and then folded using the tent transformation. For this QMC algorithm we show that the
root mean square worst-case error converges with order for any ɛ > 0, where 2
m
is the number of points. A similar result for lattice rules has previously been shown by Hickernell.
Ligia L. Cristea is supported by the Austrian Research Fund (FWF), Project P 17022-N 12 and Project S 9609.
Josef Dick is supported by the Australian Research Council under its Center of Excellence Program.
Gunther Leobacher is supported by the Austrian Research Fund (FWF), Project S 8305.
Friedrich Pillichshammer is supported by the Austrian Research Fund (FWF), Project P 17022-N 12, Project S 8305 and Project
S 9609. 相似文献
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We present a number of fast constructions of discrete Brownian paths that can be used as alternatives to principal component analysis and Brownian bridge for stratified Monte Carlo and quasi-Monte Carlo. By fast we mean that a path of length n can be generated in O(nlog(n)) floating point operations. We highlight some of the connections between the different constructions and we provide some numerical examples. 相似文献
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Josef Dick Peter Kritzer Gunther Leobacher Friedrich Pillichshammer 《Finite Fields and Their Applications》2007,13(4):1045-1070
In this paper we study construction algorithms for polynomial lattice rules modulo arbitrary polynomials. Polynomial lattice rules are a special class of digital nets which yield well distributed point sets in the unit cube for numerical integration.Niederreiter obtained an existence result for polynomial lattice rules modulo arbitrary polynomials for which the underlying point set has a small star discrepancy and recently Dick, Leobacher and Pillichshammer introduced construction algorithms for polynomial lattice rules modulo an irreducible polynomial for which the underlying point set has a small (weighted) star discrepancy.In this work we provide construction algorithms for polynomial lattice rules modulo arbitrary polynomials, thereby generalizing the previously obtained results. More precisely we use a component-by-component algorithm and a Korobov-type algorithm. We show how the search space of the Korobov-type algorithm can be reduced without sacrificing the convergence rate, hence this algorithm is particularly fast. Our findings are based on a detailed analysis of quantities closely related to the (weighted) star discrepancy. 相似文献
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Dick Josef; Leobacher Gunther; Pillichshammer Friedrich 《IMA Journal of Numerical Analysis》2007,27(4):655-674
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Monatshefte für Mathematik - Labyrinth fractals are self-similar dendrites in the unit square that are defined with the help of a labyrinth set or a labyrinth pattern. In the case when the... 相似文献