共查询到20条相似文献,搜索用时 31 毫秒
1.
Stephen James Wolfe 《Journal of multivariate analysis》1980,10(3):379-384
In 1937, Paul Lévy proved two theorems that characterize one-dimensional distribution functions of class L. In 1972, Urbanik generalized Lévy's first theorem. In this note, we generalize Lévy's second theorem and obtain a new characterization of Lévy probability distribution functions on Euclidean spaces. This result is used to obtain a new characterization of operator stable distribution functions on Euclidean spaces and to show that symmetric Lévy distribution functions on Euclidean spaces need not be symmetric unimodal. 相似文献
2.
Stephen James Wolfe 《Journal of multivariate analysis》1978,8(1):141-145
A theorem is proved that characterizes multivariate distribution functions of class L. This theorem is used to show that every n-dimensional, symmetric distribution function of class L is unimodal in the sense of Kanter. 相似文献
3.
In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems for these non-linear functions when they converge in law to a normal distribution. 相似文献
4.
We study the existence of nontrivial radial solutions for quasilinear elliptic equations with unbounded or decaying radial potentials. The existence results are based upon several new embedding theorems we establish in the paper for radially symmetric functions. 相似文献
5.
Joel Spencer 《Combinatorica》1981,1(3):303-307
We compare extremal theorems such as Turán’s theorem with their corresponding partition theorems such as Ramsey’s theorem.
We derive a general inequality involving chromatic number and independence number of symmetric hypergraphs. We give applications
to Ramsey numbers and to van der Waerden numbers. 相似文献
6.
Pedro Freitas Jing Mao Isabel Salavessa 《Calculus of Variations and Partial Differential Equations》2014,51(3-4):701-724
Given a manifold \(M\) , we build two spherically symmetric model manifolds based on the maximum and the minimum of its curvatures. We then show that the first Dirichlet eigenvalue of the Laplace–Beltrami operator on a geodesic disk of the original manifold can be bounded from above and below by the first eigenvalue on geodesic disks with the same radius on the model manifolds. These results may be seen as extensions of Cheng’s eigenvalue comparison theorems, where the model constant curvature manifolds have been replaced by more general spherically symmetric manifolds. To prove this, we extend Rauch’s and Bishop’s comparison theorems to this setting. 相似文献
7.
Alberto Lanconelli 《Mediterranean Journal of Mathematics》2005,2(4):367-379
In the present paper the Wick version of analytic functions with respect to a one dimensional Brownian motion is shown to
be closely related to the backward heat equation. This fact provides representation theorems for a certain class of random
variables in terms of Wick powers. In addition, we obtain explicit formulas for the action of some second quantization operators
arising in the applications. 相似文献
8.
Gerold Alsmeyer 《Acta Appl Math》1994,34(1-2):135-150
The present work surveys some extensions of Blackwell's renewal theorem for a certain class of linear submartingalesS
which have been recently obtained by the author. The basic assumption onS
is that their conditional increment distribution functions with respect to some filtration
are bounded from above and below by integrable distribution functions. Under a further mean stability condition these random walks turn out to be natural candidates for satisfying Blackwell-type renewal theorems. The latter are derived by employing a coupling argument similar to that which has been used in the i.i.d. case by Lindvallet al. A number of applications are also presented. 相似文献
9.
Alberto Carabarin-Aguirre 《Journal of multivariate analysis》2010,101(6):1501-1519
This paper focuses on the problem of the estimation of a distribution on an arbitrary complete separable metric space when the data points are subject to censoring by a general class of random sets. If the censoring mechanism is either totally observable or totally ordered, a reverse probability estimator may be defined in this very general framework. Functional central limit theorems are proven for the estimator when the underlying space is Euclidean. Applications are discussed, and the validity of bootstrap methods is established in each case. 相似文献
10.
11.
Sanaa Kholfi Hosam M. Mahmoud 《Statistics & probability letters》2012,82(1):49-57
In Kholfi and Mahmoud (2011) the class of tenable irreducible nondegenerate zero-balanced Pólya urn schemes is introduced and its asymptotic behavior in various phases is studied. In the absence of an initially dominant subset of colors, the counts of balls of all the colors satisfy multivariate central limit theorems. It is reported there that the case of an initially dominant subset of colors poses challenges requiring finer asymptotic analysis. In the present investigation we follow up on this. Indeed, we characterize noncritical cases with an initially dominant subset of colors in which not all ball counts satisfy one multivariate central limit theorem, but rather a subset of the ball counts satisfies a singular multivariate central limit theorem. The rest of the cases are critical, in which all the ball counts satisfy a multivariate central limit theorem, but under a different scaling. However, for these critical cases the Gaussian phases are delayed considerably. 相似文献
12.
The theory of elliptically contoured distributions is presented in an unrestricted setting, with no moment restrictions or assumptions of absolute continuity. These distributions are defined parametrically through their characteristic functions and then studied primarily through the use of stochastic representations which naturally follow from the work of Schoenberg [5] on spherically symmetric distributions. It is shown that the conditional distributions of elliptically contoured distributions are elliptically contoured, and the conditional distributions are precisely identified. In addition, a number of the properties of normal distributions (which constitute a type of elliptically contoured distributions) are shown, in fact, to characterize normality. 相似文献
13.
We derive closed form expressions and limiting formulae for a variety of functions of a permutation resulting from repeated
riffle shuffles. The results allow new formulae and approximations for the number of permutations inS
n with given cycle type and number of descents. The theorems are derived from a bijection discovered by Gessel. A self-contained
proof of Gessel's result is given. 相似文献
14.
Frédéric Chyzak 《Journal of Combinatorial Theory, Series A》2005,112(1):1-43
Many combinatorial generating functions can be expressed as combinations of symmetric functions, or extracted as sub-series and specializations from such combinations. Gessel has outlined a large class of symmetric functions for which the resulting generating functions are D-finite. We extend Gessel's work by providing algorithms that compute differential equations, these generating functions satisfy in the case they are given as a scalar product of symmetric functions in Gessel's class. Examples of applications to k-regular graphs and Young tableaux with repeated entries are given. Asymptotic estimates are a natural application of our method, which we illustrate on the same model of Young tableaux. We also derive a seemingly new formula for the Kronecker product of the sum of Schur functions with itself. 相似文献
15.
We study the evolution of a self-gravitating compressible fluid in spherical symmetry and we prove the existence of weak solutions with bounded variation for the Einstein–Euler equations of general relativity. We formulate the initial value problem in Eddington–Finkelstein coordinates and prescribe spherically symmetric data on a characteristic initial hypersurface. We introduce here a broad class of initial data which contain no trapped surfaces, and we then prove that their Cauchy development contains trapped surfaces. We therefore establish the formation of trapped surfaces in weak solutions to the Einstein equations. This result generalizes a theorem by Christodoulou for regular vacuum spacetimes (but without symmetry restriction). Our method of proof relies on a generalization of the “random choice” method for nonlinear hyperbolic systems and on a detailed analysis of the nonlinear coupling between the Einstein equations and the relativistic Euler equations in spherical symmetry. 相似文献
16.
B. Gyires 《Periodica Mathematica Hungarica》1978,9(1-2):109-113
This paper contains applications of theorems of [1] for quadratic statistics which have constant regression on linear statistics. Two theorems are proved. The first is a sufficient condition which assumes that the characteristic function of a sample is an entire function. The second gives a new characterization of the normal distribution. 相似文献
17.
Philip Feinsilver 《Acta Appl Math》1996,43(3):289-316
Representations of a complex form of the Lie algebra of the Euclidean group of the plane are found. Bases for the corresponding Hilbert spaces are given in terms of Lommel polynomials and Bessel functions. An element of the Lie algebra is interpreted as a quantum random variable leading to the Lommel distributions. The tails of these distributions and limit theorems are studied. Applications to electronic music are noted, as well as connection with quantum mechanics on a one-dimensional lattice. 相似文献
18.
Linfeng Zhou 《Geometriae Dedicata》2012,158(1):353-364
We investigate projective spherically symmetric Finsler metrics with constant flag curvature in R n and give the complete classification theorems. Furthermore, a new class of Finsler metrics with two parameters on n-dimensional disk is found to have constant negative flag curvature. 相似文献
19.
Fabio Punzo 《NoDEA : Nonlinear Differential Equations and Applications》2013,20(3):1295-1315
We prove Hadamard and Liouville type theorems for viscosity supersolutions to fully nonlinear elliptic equations on spherically symmetric complete noncompact Riemannian manifolds. 相似文献
20.
A tanglegram consists of two binary rooted trees with the same number of leaves and a perfect matching between the leaves of the trees. We show that the two halves of a random tanglegram essentially look like two independently chosen random plane binary trees. This fact is used to derive a number of results on the shape of random tanglegrams, including theorems on the number of cherries and generally occurrences of subtrees, the root branches, the number of automorphisms, and the height. For each of these, we obtain limiting probabilities or distributions. Finally, we investigate the number of matched cherries, for which the limiting distribution is identified as well. 相似文献