Journal Article10.2307/1968466
Metric spaces and completely monotone functions
1.1K
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.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Tempered Stable Ornstein-Uhlenbeck Processes: A Practical View
TL;DR: In this paper, the one-dimensional Ornstein-Uhlenbeck (OU) processes with marginal law given by the tempered stable and tempered infinitely divisible distributions proposed by Rosinski (2007) and Bianchi et al. (2010b) were studied.
28
•Journal Article
Refinement of Reproducing Kernels
Yuesheng Xu,Haizhang Zhang +1 more
TL;DR: A refinement kernels for translation invariant kernels and Hilbert-Schmidt kernels are investigated and it is shown that a nontrivial refinement kernel for a given kernel always exists if the input space has an infinite cardinal number.
28
Isotropic covariance matrix functions on all spheres
TL;DR: In this paper, the authors introduce characterizations of the covariance function on all spheres that is isotropic and continuous and derive some covariance (matrix) structures with certain polynomials obtained.
28
Approximate Minimization of the Regularized Expected Error over Kernel Models
Věra Kůrková,Marcello Sanguineti +1 more
TL;DR: Learning from data under constraints on model complexity is studied in terms of rates of approximate minimization of the regularized expected error functional, and upper bounds on such rates are derived.
28
Singular elliptical distribution: density and applications
TL;DR: In this article, an explicit expression for the density of a n-dimensional random vector with a singular Elliptical distribution was presented. And the densities of generalized Chi-squared and generalized t distributions were derived, examining the Pearson Type VII distribution and Kotz Type distribution.
27
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.
492
•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.
486