Distribution functions of ratio sequences, IV

Baláž, Vladimír; Mišík, Ladislav; Strauch, Oto; Tóth, János T.

doi:10.1007/s10998-013-4116-4

Cited by 6 publications

(13 citation statements)

References 2 publications

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“…More recently, the study of distribution functions was extended to multivariate functions by the Slovak school of O. Strauch and his coworkers; see [5,6,24,44]. In particular, they studied properties of the set of distribution functions of sequences in [0, 1] 2 and various extremal problems related to distribution functions.…”

Section: Introductionmentioning

confidence: 99%

Distribution functions, extremal limits and optimal transport

Iacò

Thonhauser

Tichy

2015

Indagationes Mathematicae

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Encouraged by the study of extremal limits for sums of the formwith uniformly distributed sequences {xn}, {yn} the following extremal problem is of interestfor probability measures γ on the unit square with uniform marginals, i.e., measures whose distribution function is a copula. The aim of this article is to relate this problem to combinatorial optimization and to the theory of optimal transport. Using different characterizations of maximizing γ's one can give alternative proofs of some results from the field of uniform distribution theory and beyond that treat additional questions. Finally, some applications to mathematical finance are addressed.

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Section: Introductionmentioning

confidence: 99%

Distribution functions, extremal limits and optimal transport

Iacò

Thonhauser

Tichy

2015

Indagationes Mathematicae

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“…2 dx → 0. This gives (4). The existence of the limit lim k→∞ n k m k = α < ∞ follows from (1) and (iv).…”

Section: Basic Propertiesmentioning

confidence: 79%

“…Basic open problem is that characterize a nonempty set H of d.f.s for which there exists an increasing sequence of positive integers x n such that G(X n ) = H. In [3] we found integer sequence 1 ≤ x 1 < x 2 < • • • such that the piecewise linear function h 2 (x) defined in (19) belongs to G(X n ). In [4] is the following extension of this construction:…”

Section: Construction H ⊂ G(x N )mentioning

confidence: 99%

Distribution functions of ratio sequences. An expository paper

Strauch

2015

Tatra Mountains Mathematical Publications

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This expository paper presents known results on distribution functions g(x) of the sequence of blocks where xn is an increasing sequence of positive integers. Also presents results of the set G(Xn) of all distribution functions g(x). Specially: - continuity of g(x); - connectivity of G(Xn); - singleton of G(Xn); - one-step g(x); - uniform distribution of Xn, n = 1, 2, . . . ; - lower and upper bounds of g(x); - applications to bounds of ; - many examples, e.g., , where pn is the nth prime, is uniformly distributed. The present results have been published by 25 papers of several authors between 2001-2013.

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“…. The set of distribution functions of ratio block sequences was studied in [1][2][3][4][5][6][7][9][10][11][12].…”

Section: Definitionsmentioning

confidence: 99%