共查询到20条相似文献,搜索用时 15 毫秒
1.
R. I. Kozlov 《Siberian Mathematical Journal》2013,54(5):817-828
We generalize asymptotic stability criteria and estimates for attraction domains in the nonnegative cone for systems of autonomous difference equations with monotone discontinuous right-hand side. 相似文献
2.
It is shown that for exponential Lie groupsG the limit behavior of i.i.d. triangular arrays on the groupG and on the tangent spaceG coincide. This result is used to obtain a characterization of domains of partial attraction (resp. semistable attraction) on exponential (resp. simply connected nilpotent) Lie groups via the corresponding domains on the tangent space. 相似文献
3.
Mark M. Meerschaert 《Journal of Theoretical Probability》1994,7(4):793-798
A sequence of independent and identically distributed random vectorsX
n
on
k
is said to belong to the generalized domain of attraction of a nondegenerate random vectorY on
k
provided that there exist linear operatorsA
n
on
k
and nonrandom constantsb
n
k
such that the centered and normalized partial sumsA
n
(X
1++X
n
–b
n
converge in distribution toY. In this paper we show that the sequence of norming operatorsA
n
can always be chosen to vary regularly.Partially supported by NSF Grant DMS-91-03131 at Albion College. 相似文献
4.
《Journal of Applied Mathematics and Mechanics》1999,63(4):545-555
Linear Hamiltonian systems with an arbitrary number of degrees of freedom, which depend smoothly on a vector of real parameters, are investigated. All possible singularities of the boundary of the stability domain of Hamiltonian systems of general position are determined and described for the case of two and three parameters. In the first approximation, the geometry of these singularities (the orientation in the parameter space, angles, etc.) is determined on the basis of the first derivative of the matrix of the system with respect to the parameters, as are the eigenvectors and generalized eigenvectors evaluated at the singular point. A detailed investigation is made of gyroscopic systems as a special case of Hamiltonian systems. As mechanical examples, an account is given of the problem of the stability of the oscillations of a tube through which a fluid is flowing, and of the stability of the motion of a two-body system. The tangent cones to the stability domains of these systems at singular points of the “cusp” and “dihedral angle” type, which arise on the boundaries of these domains, are found. 相似文献
5.
Let X,X1,X2,… be independent and identically distributed Rd-valued random vectors and assume X belongs to the generalized domain of attraction of some operator semistable law without normal component. Then without changing its distribution, one can redefine the sequence on a new probability space such that the properly affine normalized partial sums converge in probability and consequently even in Lp (for some p>0) to the corresponding operator semistable Lévy motion. 相似文献
6.
Bivariate stable distributions are defined as those having a domain of attraction, where vectors are used for normalization. These distributions are identified and their domains of attraction are given in a number of equivalent forms. In one case, marginal convergence implies joint convergence. A bivariate optional stopping property is given. Applications to bivariate random walk are suggested. 相似文献
7.
LetX,X
1,X
2,... be i.i.d. random vectors in d. The limit laws that can arise by suitable affine normalizations of the partial sums,S
n=X
1+...+X
n, are calledoperator-stable laws. These laws are a natural extension to
d
of the stable laws on. Thegeneralized domain of attraction of [GDOA()] is comprised of all random vectorsX whose partial sums can be affinely normalized to converge to . If the linear part of the affine transformation is restricted to take the formn
–B for some exponent operatorB naturally associated to thenX is in thegeneralized domain of normal attraction of [GDONA()]. This paper extends the theory of operator-stable laws and their domains of attraction and normal attraction. 相似文献
8.
9.
10.
Convolution tails,product tails and domains of attraction 总被引:7,自引:0,他引:7
Daren B. H. Cline 《Probability Theory and Related Fields》1986,72(4):529-557
Summary A distribution function is said to have an exponential tail F(t) = F(t, ) if e
u
F(t+u) is asymptotically equivalent to F(t), t, t, for all u. In this case F(lnt) is regularly varying. For two such distributions, F and G, the convolution H=F*G also has an exponential tail. We investigate the relationship between H and its components F and G, providing conditions for lim H/F to exist. In addition, we are able to describe the asymptotic nature of H when the limit is infinite, for many cases. This corresponds to determining both the domain of attraction and the norming constants for the product of independent variables whose distributions have regularly varying tails.In addition, we compare the tails of H=F*G with H
1=F
1*G
1when F is asymptotically equivalent to F and G is equivalent to G
1. Such a comparison corresponds to the balancing consideration for the product of independent variables in stable domains of attraction. We discover that there are several distinct comparisons possible. 相似文献
11.
For a convex body K in ℝn, the volume quotient is the ratio of the smallest volume of the circumscribed ellipsoids to the largest volume of the inscribed
ellipsoids, raised to power 1/n. It attains its maximum if and only if K is a simplex. We improve this result by estimating the Banach-Mazur distance of K from a simplex if the volume quotient of K is close to the maximum.
This work was supported in part by the European Network PHD, FP6 Marie Curie Actions, RTN, Contract MCRN-511953. 相似文献
12.
We study the behavior of a quasi-geostrophic flow in thef-plane. We consider a positive initial potential vorticity with a compact support and we bound the growth in time of its support. We prove also that a fluid particle cannot go fast away from the initial position. 相似文献
13.
14.
H. -P. Scheffler 《Journal of Mathematical Sciences》1998,92(4):4062-4084
The goal of this paper is to extend the series representation to operator semistable laws and to give necessary and sufficient
conditions for a vector X to belong to the generalized domain of normal attraction of some operator semistable law having
no Gaussian component.
Proceedings of the Seminar on Stability Problems for Stochastic Models. Hajdúszoboszló. Hungary 1997, Part II. 相似文献
15.
Summary Each probability measure C on a first orthant is associated with a harmonic renewal measure G. Specifically we consider (N, S
N
) the ladder (time, place) of a random walk S
n. Using bivariate G we show that when S
1 is in a domain of attraction so is (N, S
N). This unifies and generalizes results of Sinai, Rogosin. 相似文献
16.
Peter W. Conrad William O. Criminale Jr. 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1965,16(2):233-254
Zusammenfassung In dieser Arbeit wird das allgemeine Problem der Stabilität inkompressibler, instationärer, paralleler und laminarer Strömungen zwischen zwei unendlichen Ebenen untersucht. Dabei werden sowohl die klassische linearisierte Theorie für Störungen mit kleiner Amplitude als auch eine Variationsmethode für Störungen endlicher Grösse angewandt. Die grundlegenden Lehrsätze der linearen Theorie werden, soweit dies für das allgemeine Problem möglich ist, erweitert und ihre Konsequenzen aufgezeigt. Unter Anwendung der Variationsmethode werden für mehrere besondere instationäre Strömungen quantitative Ergebnisse gezeigt, aber die hier entwickelten Gleichungen können ebenso auf jedwede parallele Strömung angewendet werden. Das stationäre Problem ist als ein besonderer Grenzfall behandelt. 相似文献
17.
If the centered and normalized partial sums of an i.i.d. sequence of random variables converge in distribution to a nondegenerate limit then we say that this sequence belongs to the domain of attraction of the necessarily stable limit. If we consider only the partial sums which terminate atk
n
wherek
n+1
ck
n
then the sequence belongs to the domain of semistable attraction of the necessarily semistable limit. In this paper, we consider the case where the limiting distribution is nonnormal. We obtain a series representation for the partial sums which converges almost surely. This representation is based on the order statistics, and utilizes the Poisson process. Almost sure convergence is a useful technical device, as we illustrate with a number of applications.This research was supported by a research scholarship from the Deutsche Forschungsgemeinschaft (DFG). 相似文献
18.
István Berkes 《Probability Theory and Related Fields》1995,102(1):1-17
We give necessary and sufficient criteria for a sequence (X
n) of i.i.d. r.v.'s to satisfy the a.s. central limit theorem, i.e.,
相似文献
19.
《Journal of Applied Mathematics and Mechanics》2003,67(2):209-213
The stability of mechanical systems, on which dissipative, gyroscopic, potential and positional non-conservative forces act, is investigated. The condition for asymptotic stability is obtained using the Lyapunov function and an estimate of the domain of attraction is also found in terms of the system being considered. A precessional system is also examined. It is shown that the condition for the asymptotic stability of a system is the condition of acceptability in the sense of the stability of a precessional system. The results obtained are applied to the problem of the stabilization, using external moments, of the steady motion of a balanced gyroscope in gimbals. 相似文献
20.
《Journal of Applied Mathematics and Mechanics》1999,63(2):323-326
The results obtained in [1–5] are applied to give a criterion for the stability of the equilibrium states of systems with a delay at points on the boundaries of stability domains where safe sections become unsafe. 相似文献
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