Journal Article10.2307/1968466
Metric spaces and completely monotone functions
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About: This article is published in Annals of Mathematics. The article was published on 01 Oct 1938. The article focuses on the topics: Convex metric space & Injective metric space.
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Citations
Differentiability of bizonal positive definite kernels on complex spheres
TL;DR: In this paper, it was shown that any continuous function with domain { z ∈ C : | z | ⩽ 1 } that generates a bizonal positive definite kernel on the unit sphere in C q, q ⩾ 3, is continuous differentiable in { z − 2, with respect to both z and z ¯.
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Extrapolation of Stationary Random Fields
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Simulating space-time random fields with nonseparable Gneiting-type covariance functions
TL;DR: Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial structure and a conditionally negative definite functionassociated with the temporal structure.
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The Gauss Hypergeometric Covariance Kernel for Modeling Second-Order Stationary Random Fields in Euclidean Spaces: its Compact Support, Properties and Spectral Representation
Xavier Emery,Alfredo Alegría +1 more
TL;DR: In this paper, a parametric family of compactly-supported positive semidefinite kernels aimed to model the covariance structure of second-order stationary isotropic random fields defined in the $d$-dimensional Euclidean space is presented.
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Squaring the Circle and Cubing the Sphere: Circular and Spherical Copulas
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References
Metric spaces and positive definite functions
TL;DR: In this paper, a connection between the problem of isometric imbedding and the concept of positive definite functions has been made, and it has been shown that the possibility of topological imbeddability of (E in '&) is very easily expressible in terms of the elementary function e-t2 and positive definite function (Theorem 1) if this concept is properly enlarged.
Sur les fonctions absolument monotones
TL;DR: Les fonctions absolument monotones jouent le m~me rble fondamenta l duns la th6orie des f o n c t i o n s analytiques d 'une variable r6elle que les fonsctions (simplement) monotone for la classe g6n6rale des fonction £ variat ion born6e as mentioned in this paper.
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•Book
Random variables and probability distributions
Harald Cramér
- 01 Jan 1937
TL;DR: In this paper, the authors introduce Axioms and preliminary theorems of the central limit theorem for stochastic processes and the normal distribution of the distribution in R1 and R2.
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