共查询到20条相似文献,搜索用时 140 毫秒
1.
Let the random vector (X,Y) follow a bivariate Sarmanov distribution, where X is real-valued and Y is nonnegative. In this paper we investigate the impact of such a dependence structure between X and Y on the tail behavior of their product Z?=?XY. When X has a regularly varying tail, we establish an asymptotic formula, which extends Breiman’s theorem. Based on the obtained result, we consider a discrete-time insurance risk model with dependent insurance and financial risks, and derive the asymptotic and uniformly asymptotic behavior for the (in)finite-time ruin probabilities. 相似文献
2.
We consider the random difference equations S = d (X + S)Y and T = d X + TY, where = d denotes equality in distribution, X and Y are two nonnegative random variables, and S and T on the right-hand side are independent of (X, Y). Under the assumptions that X follows a subexponential distribution with a nonzero lower Karamata index, that Y takes values in [0, 1] and is not degenerate at 0 or 1, and that (X, Y) fulfills a certain dependence structure via the conditional tail probability of X given Y, we derive some asymptotic formulas for the tail probabilities of the weak solutions S and T to these equations. In doing so we also obtain some by-products which are interesting in their own right. 相似文献
3.
The Erd?s-Trost problem can be formulated in the following way: “If the triangle XY Z is inscribed in the triangle ABC—with X, Y, and Z on the sides BC, CA, and AB, respectively—then one of the areas of the triangles BXZ, CXY , AY Z is less than or equal to the area of the triangle XY Z.” There are many different solutions for this problem. In this note we take up a very elementary proof (due to Szekeres) and deduce that the class of ordered translation planes is the level in the hierarchy of affine planes where the Erd?s-Trost statement still holds true. We also look at the conditions an absolute plane needs to satisfy for the validity of the Erd?s-Trost statement. 相似文献
4.
G. Rebelles 《Mathematical Methods of Statistics》2016,25(1):26-53
In this paper, we address the problem of estimating a multidimensional density f by using indirect observations from the statistical model Y = X + ε. Here, ε is a measurement error independent of the random vector X of interest and having a known density with respect to Lebesgue measure. Our aim is to obtain optimal accuracy of estimation under \({\mathbb{L}_p}\)-losses when the error ε has a characteristic function with a polynomial decay. To achieve this goal, we first construct a kernel estimator of f which is fully data driven. Then, we derive for it an oracle inequality under very mild assumptions on the characteristic function of the error ε. As a consequence, we getminimax adaptive upper bounds over a large scale of anisotropic Nikolskii classes and we prove that our estimator is asymptotically rate optimal when p ∈ [2,+∞]. Furthermore, our estimation procedure adapts automatically to the possible independence structure of f and this allows us to improve significantly the accuracy of estimation. 相似文献
5.
Let G be a finite group. If Mn< Mn?1< · · · < M1< M0 = G with Mi a maximal subgroup of Mi?1 for all i = 1,..., n, then Mn (n > 0) is an n-maximal subgroup of G. A subgroup M of G is called modular provided that (i) 〈X,M ∩ Z〉 = 〈X,M〉 ∩ Z for all X ≤ G and Z ≤ G such that X ≤ Z, and (ii) 〈M,Y ∩ Z〉 = 〈M,Y 〉 ∩ Z for all Y ≤ G and Z ≤ G such that M ≤ Z. In this paper, we study finite groups whose n-maximal subgroups are modular. 相似文献
6.
M. F. Prokhorova 《Proceedings of the Steklov Institute of Mathematics》2014,287(1):156-166
We investigate equations of the form D t u = Δu + ξ? u for an unknown function u(t, x), t ∈ ?, x ∈ X, where D t u = a 0(u, t) + Σ k=1 r a k (t, u)? t k u, Δ is the Laplace-Beltrami operator on a Riemannian manifold X, and ξ is a smooth vector field on X. More exactly, we study morphisms from this equation within the category PDE of partial differential equations, which was introduced by the author earlier. We restrict ourselves to morphisms of a special form—the so-called geometric morphisms, which are given by maps of X to other smooth manifolds (of the same or smaller dimension). It is shown that a map f: X → Y defines a morphism from the equation D t u = Δu + ξ? u if and only if, for some vector field Ξ and a metric on Y, the equality (Δ + ξ?)f*v = f*(Δ + Ξ?)v holds for any smooth function v: Y → ?. In this case, the quotient equation is D t v = Δv + Ξ?v for an unknown function v(t, y), y ∈ Y. It is also shown that, if a map f: X → Y is a locally trivial bundle, then f defines a morphism from the equation D t u = Δu if and only if fibers of f are parallel and, for any path γ on Y, the expansion factor of a fiber translated along the horizontal lift γ to X depends on γ only. 相似文献
7.
Let (X, Y) be a balanced pair in an abelian category. We first introduce the notion of cotorsion pairs relative to (X, Y), and then give some equivalent characterizations when a relative cotorsion pair is hereditary or perfect. We prove that if the X-resolution dimension of Y (resp. Y-coresolution dimension of X) is finite, then the bounded homotopy category of Y (resp. X) is contained in that of X (resp. Y). As a consequence, we get that the right X-singularity category coincides with the left Y-singularity category if the X-resolution dimension of Y and the Y-coresolution dimension of X are finite. 相似文献
8.
Timur Oikhberg 《Archiv der Mathematik》2017,109(3):245-253
A classical problem (initially studied by N. Kalton and A. Wilansky) concerns finding closed infinite dimensional subspaces of X / Y, where Y is a subspace of a Banach space X. We study the Banach lattice analogue of this question. For a Banach lattice X, we prove that X / Y contains a closed infinite dimensional sublattice under the following conditions: either (i) Y is a closed infinite codimensional subspace of X, and X is either order continuous or a C(K) space, where K is a compact subset of \({\mathbb {R}}^n\); or (ii) Y is the range of a compact operator. 相似文献
9.
Let X and Y be completely regular spaces and E and F be Hausdorff topological vector spaces. We call a linear map T from a subspace of C(X, E) into C(Y, F) a Banach–Stone map if it has the form T f (y) = S y (f (h(y))) for a family of linear operators S y : E → F, \({y \in Y}\) , and a function h: Y → X. In this paper, we consider maps having the property: where Z(f) = {f = 0}. We characterize linear bijections with property (Z) between spaces of continuous functions, respectively, spaces of differentiable functions (including C ∞), as Banach–Stone maps. In particular, we confirm a conjecture of Ercan and Önal: Suppose that X and Y are realcompact spaces and E and F are Hausdorff topological vector lattices (respectively, C *-algebras). Let T: C(X, E) → C(Y, F) be a vector lattice isomorphism (respectively, *-algebra isomorphism) such thatThen X is homeomorphic to Y and E is lattice isomorphic (respectively, C *-isomorphic) to F. Some results concerning the continuity of T are also obtained.
相似文献
$\bigcap^{k}_{i=1}Z(f_{i}) \neq\emptyset \iff \bigcap^{k}_{i=1}Z(Tf_{i})\neq\emptyset , \quad({\rm Z}) $
$ Z(f) \neq\emptyset\iff Z(Tf) \neq\emptyset. $
10.
Kai Gu 《Archiv der Mathematik》2018,111(1):57-60
Let X and Y be metric spaces with X separable, and let \(f: X\rightarrow Y\) be a Borel function. Is then f(X) separable? In this paper, we prove that this problem is independent of ZFC. We also give a partial answer to an open problem which was asked by A. H. Stone. 相似文献
11.
In this paper, we essentially compute the set of x,y>0 such that the mapping \(z\longmapsto(1-r+re^{z})^{x}(\frac{\lambda}{\lambda-z})^{y}\) is a Laplace transform. If X and Y are two independent random variables which have respectively Bernoulli and Gamma distributions, we denote by μ the distribution of X+Y. The above problem is equivalent to finding the set of x>0 such that μ *x exists. 相似文献
12.
On operators which attain their norm 总被引:1,自引:0,他引:1
Joram Lindenstrauss 《Israel Journal of Mathematics》1963,1(3):139-148
The following problem is considered. LetX andY be Banach spaces. Are those operators fromX toY which attain their norm on the unit cell ofX, norm dense in the space of all operators fromX toY? It is proved that this is always the case ifX is reflexive. In general the answer is negative and it depends on some convexity and smoothness properties of the unit cells inX andY. As an application a refinement of the Krein-Milman theorem and Mazur’s theorem concerning the density of smooth points, in the case of weakly compact sets in a separable space, is obtained. 相似文献
13.
Yan-Kui Song 《Czechoslovak Mathematical Journal》2007,57(1):387-394
In this paper, we prove the following statements: (1) For every regular uncountable cardinal κ, there exist a Tychonoff space X and Y a subspace of X such that Y is both relatively absolute star-Lindelöf and relative property (a) in X and e(Y, X) ? κ, but Y is not strongly relative star-Lindelöf in X and X is not star-Lindelöf. (2) There exist a Tychonoff space X and a subspace Y of X such that Y is strongly relative star-Lindelöf in X (hence, relative star-Lindelöf), but Y is not absolutely relative star-Lindelöf in X. 相似文献
14.
Tim Netzer 《Journal of Geometric Analysis》2010,20(3):751-770
We consider a closed set S?? n and a linear operator that preserves nonnegative polynomials, in the following sense: if f≥0 on S, then Φ(f)≥0 on S as well. We show that each such operator is given by integration with respect to a measure taking nonnegative functions as its values. This can be seen as a generalization of Haviland’s Theorem, which concerns linear functionals on ?[X 1,…,X n ]. For compact sets S we use the result to show that any nonnegativity preserving operator is a pointwise limit of very simple nonnegativity preservers with finite dimensional range.
相似文献
$\Phi \colon \mathbb{R}[X_1,\ldots,X_n]\rightarrow \mathbb{R}[X_1,\ldots,X_n]$
15.
Yu. Golubev 《Mathematical Methods of Statistics》2018,27(3):205-225
The paper considers a simple Errors-in-Variables (EiV) model Yi = a + bXi + εξi; Zi= Xi + σζi, where ξi, ζi are i.i.d. standard Gaussian random variables, Xi ∈ ? are unknown non-random regressors, and ε, σ are known noise levels. The goal is to estimates unknown parameters a, b ∈ ? based on the observations {Yi, Zi, i = 1, …, n}. It is well known [3] that the maximum likelihood estimates of these parameters have unbounded moments. In order to construct estimates with good statistical properties, we study EiV model in the large noise regime assuming that n → ∞, but \({\epsilon ^2} = \sqrt n \epsilon _ \circ ^2,{\sigma ^2} = \sqrt n \sigma _ \circ ^2\) with some \(\epsilon_\circ^2, \sigma_\circ^2>0\). Under these assumptions, a minimax approach to estimating a, b is developed. It is shown that minimax estimates are solutions to a convex optimization problem and a fast algorithm for solving it is proposed. 相似文献
16.
We first consider a real random variable X represented through a random pair (R,T) and a deterministic function u as X = R?u(T). Under quite weak assumptions we prove a limit theorem for (R,T) given X>x, as x tends to infinity. The novelty of our paper is to show that this theorem for the representation of the univariate random variable X permits us to obtain in an elegant manner conditional limit theorems for random pairs (X,Y) = R?(u(T),v(T)) given that X is large. Our approach allows to deduce new results as well as to recover under considerably weaker assumptions results obtained previously in the literature. Consequently, it provides a better understanding and systematization of limit statements for the conditional extreme value models. 相似文献
17.
For X, Y ∈ Mn,m it is said that X is gut-majorized by Y, and we write X ?gutY, if there exists an n-by-n upper triangular g-row stochastic matrix R such that X = RY. Define the relation ~gut as follows. X ~gutY if X is gut-majorized by Y and Y is gut-majorized by X. The (strong) linear preservers of ?gut on ?n and strong linear preservers of this relation on Mn,m have been characterized before. This paper characterizes all (strong) linear preservers and strong linear preservers of ~gut on ?n and Mn,m. 相似文献
18.
Jonas Kazys Sunklodas 《Lithuanian Mathematical Journal》2017,57(2):244-258
We present upper bounds of the integral \( {\int}_{-\infty}^{\infty }{\left|x\right|}^l\left|\mathbf{P}\left\{{Z}_N<x\right\}-\varPhi (x)\right|\mathrm{d}x \) for 0 ≤ l ≤ 1 + δ, where 0 < δ ≤ 1, Φ(x) is a standard normal distribution function, and Z N = \( {S}_N/\sqrt{\mathbf{V}{S}_N} \) is the normalized random sum with variance V S N > 0 (S N = X 1 + · · · + X N ) of centered independent random variables X 1 ,X 2 , . . . . The number of summands N is a nonnegative integer-valued random variable independent of X 1 ,X 2 , . . . . 相似文献
19.
Let X and Y be two Banach spaces, and f: X → Y be a standard ε-isometry for some ε ≥ 0. In this paper, by using a recent theorem established by Cheng et al. (2013–2015), we show a sufficient condition guaranteeing the following sharp stability inequality of f: There is a surjective linear operator T: Y → X of norm one so that
$$\left\| {Tf(x) - x} \right\| \leqslant 2\varepsilon , for all x \in X.$$
As its application, we prove the following statements are equivalent for a standard ε-isometry f: X → Y:
This gives an affirmative answer to a question proposed by Vestfrid (2004, 2015). 相似文献
- (i)lim inf t→∞ dist(ty, f(X))/|t| < 1/2, for all y ∈ S Y ;
- (ii)\(\tau(f)\equiv sup_{y\epsilon S_{Y}}\) lim inf t→∞dist(ty, f(X))/|t| = 0;
- (iii)there is a surjective linear isometry U: X → Y so that$$\left\| {f(x) - Ux} \right\| \leqslant 2\varepsilon , for all x \in X.$$
20.
The paper deals with recovering an unknown vector β ∈ ? p based on the observations Y = Xβ + ? ξ and Z = X + σζ, where X is an unknown n × p matrix with n ≥ p, ξ ∈ ? p is a standard white Gaussian noise, ζ is an n × p matrix with i.i.d. standard Gaussian entries, and ?, σ ∈ ?+ are known noise levels. It is assumed that X has a large condition number and p is large. Therefore, in order to estimate β, the simple Tikhonov–Phillips regularization (ridge regression) with a data-driven regularization parameter is used. For this estimation method, we study the effect of noise σζ on the quality of recovering Xβ using concentration inequalities for the prediction error. 相似文献