About the density of spectral measure of the two-dimensional SaS random vector

Marta Borowiecka-Olszewska; Jolanta K. Misiewicz

Displaying similar documents to “About the density of spectral measure of the two-dimensional SaS random vector”

Universal stability of Banach spaces for ε -isometries

Lixin Cheng, Duanxu Dai, Yunbai Dong, Yu Zhou (2014)

Studia Mathematica

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Let X, Y be real Banach spaces and ε > 0. A standard ε-isometry f: X → Y is said to be (α,γ)-stable (with respect to $T : L (f) \equiv \bar{s p a n} f (X) \to X$ for some α,γ > 0) if T is a linear operator with ||T|| ≤ α such that Tf- Id is uniformly bounded by γε on X. The pair (X,Y) is said to be stable if every standard ε-isometry f: X → Y is (α,γ)-stable for some α,γ > 0. The space X[Y] is said to be universally left [right]-stable if (X,Y) is always stable for every Y[X]. In this paper, we show that universally...

On stable currents in positively pinched curved hypersurfaces

Jintang Li (2003)

Colloquium Mathematicae

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Let Mⁿ (n ≥ 3) be an n-dimensional complete hypersurface in a real space form N(c) (c ≥ 0). We prove that if the sectional curvature $K_{M}$ of M satisfies the following pinching condition: $c + δ < K_{M} \leq c + 1$ , where δ = 1/5 for n ≥ 4 and δ = 1/4 for n = 3, then there are no stable currents (or stable varifolds) in M. This is a positive answer to the well-known conjecture of Lawson and Simons.

α-stable random walk has massive thorns

Alexander Bendikov, Wojciech Cygan (2015)

Colloquium Mathematicae

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We introduce and study a class of random walks defined on the integer lattice $ℤ^{d}$ -a discrete space and time counterpart of the symmetric α-stable process in $ℝ^{d}$ . When 0 < α <2 any coordinate axis in $ℤ^{d}$ , d ≥ 3, is a non-massive set whereas any cone is massive. We provide a necessary and sufficient condition for a thorn to be a massive set.

On the stability for pancyclicity

Ingo Schiermeyer (2001)

Discussiones Mathematicae Graph Theory

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A property P defined on all graphs of order n is said to be k-stable if for any graph of order n that does not satisfy P, the fact that uv is not an edge of G and that G + uv satisfies P implies $d_{G} (u) + d_{G} (v) < k$ . Every property is (2n-3)-stable and every k-stable property is (k+1)-stable. We denote by s(P) the smallest integer k such that P is k-stable and call it the stability of P. This number usually depends on n and is at most 2n-3. A graph of order n is said to be pancyclic if it contains cycles...

Uniform upper bound for a stable measure of a small ball.

Ryznar, Michał, Żak, Tomasz (1998)

Electronic Communications in Probability [electronic only]

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Generalized madogram and pairwise dependence of maxima over two regions of a random field

Cecília Fonseca, Luísa Pereira, Helena Ferreira, Ana Paula Martins (2015)

Kybernetika

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Spatial environmental processes often exhibit dependence in their large values. In order to model such processes their dependence properties must be characterized and quantified. In this paper we introduce a measure that evaluates the dependence among extreme observations located in two disjoint sets of locations of $ℝ^{2}$ . We compute the range of this new dependence measure, which extends the existing $λ$ -madogram concept, and compare it with extremal coefficients, finding generalizations...

Approximation of a symmetric α-stable Lévy process by a Lévy process with finite moments of all orders

Z. Michna (2007)

Studia Mathematica

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In this paper we consider a symmetric α-stable Lévy process Z. We use a series representation of Z to condition it on the largest jump. Under this condition, Z can be presented as a sum of two independent processes. One of them is a Lévy process $Y_{x}$ parametrized by x > 0 which has finite moments of all orders. We show that $Y_{x}$ converges to Z uniformly on compact sets with probability one as x↓ 0. The first term in the cumulant expansion of $Y_{x}$ corresponds to a Brownian motion which implies...

Large deviations in spaces of stable type

Evarist Giné (1983)

Annales de l'I.H.P. Probabilités et statistiques

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Geometric infinite divisibility, stability, and self-similarity: an overview

Tomasz J. Kozubowski (2010)

Banach Center Publications

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The concepts of geometric infinite divisibility and stability extend the classical properties of infinite divisibility and stability to geometric convolutions. In this setting, a random variable X is geometrically infinitely divisible if it can be expressed as a random sum of $N_{p}$ components for each p ∈ (0,1), where $N_{p}$ is a geometric random variable with mean 1/p, independent of the components. If the components have the same distribution as that of a rescaled X, then X is (strictly) geometric...

Almost multiplicative functionals

Krzysztof Jarosz (1997)

Studia Mathematica

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A linear functional F on a Banach algebra A is almost multiplicative if |F(ab) - F(a)F(b)| ≤ δ∥a∥ · ∥b∥ for a,b ∈ A, for a small constant δ. An algebra is called functionally stable or f-stable if any almost multiplicative functional is close to a multiplicative one. The question whether an algebra is f-stable can be interpreted as a question whether A lacks an almost corona, that is, a set of almost multiplicative functionals far from the set of multiplicative functionals. In this paper...

Potential theory of one-dimensional geometric stable processes

Tomasz Grzywny, Michał Ryznar (2012)

Colloquium Mathematicae

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The purpose of this paper is to find optimal estimates for the Green function and the Poisson kernel for a half-line and intervals of the geometric stable process with parameter α ∈ (0,2]. This process has an infinitesimal generator of the form $- l o g (1 + {(- Δ)}^{α / 2})$ . As an application we prove the global scale invariant Harnack inequality as well as the boundary Harnack principle.

Vector Optimization Results for $ℓ$ -Stable Data

Marie Dvorská (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The aim of this paper is to summarize basic facts about $ℓ$ -stable at a point vector functions and existing results for certain vector constrained programming problem with $ℓ$ -stable data.

(H,k) stable bipartite graphs with minimum size

Aneta Dudek, Małgorzata Zwonek (2009)

Discussiones Mathematicae Graph Theory

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Let us call a graph G(H;k) vertex stable if it contains a subgraph H after removing any of its k vertices. In this paper we are interested in finding the $(K_{n, n + 1}; 1)$ (respectively $(K_{n, n}; 1)$ ) vertex stable graphs with minimum size.

Existence of the fundamental solution of a second order evolution equation

Jan Bochenek (1997)

Annales Polonici Mathematici

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We give sufficient conditions for the existence of the fundamental solution of a second order evolution equation. The proof is based on stable approximations of an operator A(t) by a sequence $A_{n} (t)$ of bounded operators.

Global stability for diagrams of differentiable applications

Luis Antonio Favaro, C. M. Mendes (1986)

Annales de l'institut Fourier

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In this paper, we give some examples which point to the non-existence of $C^{\infty}$ -global stable diagrams $R \overset{g}{\leftarrow} M \overset{f}{\to} R$ , $M$ compact. If $Φ$ : $M \to Q$ is fixed we define the $Φ$ -equivalence for maps $f : M \to P$ and the corresponding $Φ$ -stability. The globalization procedure works and we can compare the $Φ$ -stability, $Φ$ -infinitesimal stability, and $Φ$ -homotopical stability. Also we give some characterization theorems for lower dimensions.

Характеризация $ω$ -стабильных теорий ограниченной размерности

Т.А. Нурмагамбетов (1989)

Algebra i Logika

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Stable cohomotopy groups of compact spaces

Sławomir Nowak (2003)

Fundamenta Mathematicae

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We show that one can reduce the study of global (in particular cohomological) properties of a compact Hausdorff space X to the study of its stable cohomotopy groups $π_{s}^{k} (X)$ . Any cohomology functor on the homotopy category of compact spaces factorizes via the stable shape category ShStab. This is the main reason why the language and technique of stable shape theory can be used to describe and analyze the global structure of compact spaces. For a given Hausdorff compact space X, there exists...