共查询到20条相似文献,搜索用时 15 毫秒
1.
W. T. Van Horssen 《Journal of Difference Equations and Applications》2013,19(12):1133-1146
In this paper, the concept of invariance factors and invariance vectors to obtain invariants (or first integrals) for difference equations will be presented. It will be shown that all invariance factors and invariance vectors have to satisfy a functional equation. This concept turns out to be analogous to the concept of integrating factors and integrating vectors for ordinary differential equations. 相似文献
2.
《Applied Mathematics Letters》2003,16(1):85-91
In this paper, we derive an invariance principle generalizing LaSalle's invariance principle for discrete-time nonlinear systems. Next, using the invariance principle, we develop a series of results relating stability, observability, and converse Lyapunov theorems for discrete-time nonlinear systems. 相似文献
3.
A. G. Tumanyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2016,51(4):187-198
The paper is devoted to the questions of invariance of the index of a semielliptical operator on the scale of anisotropic spaces. A necessary and sufficient condition for the invariance of the index of a linear bounded operator on the embedded Hilbert spaces is obtained. This condition is applied to study the invariance of the index of a semielliptical operator. For a semielliptical operator a sufficient condition for the invariance of the index on the scale of anisotropic spaces is obtained. 相似文献
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Our aim is to investigate a way to characterize the elements of a statistical manifold (the metric and the family of connections) using invariance properties suggested by Le Cam's theory of experiments. We distinguish the case where the statistical manifold is flat. Then, there naturally exists an entropy and it is proven that experiment invariance is equivalent to entropy invariance. If the statistical manifold is not flat, we introduce a notion of local invariance of selected order associated to the asymptotic (on n observations, n tending to infinity) expansion of the power of the Neymann Pearson test in a contiguous neighborough of some point. This invariance provides a substantial number of morphisms. This was not always true for the entropy invariance: particularly, the case of Gaussian experiments is investigated where it can be proven that entropy invariance does not characterize a metric or a family of connections. 相似文献
6.
Reinaldo B. Arellano-Valle Marc G. Genton 《Annals of the Institute of Statistical Mathematics》2010,62(2):363-381
We study conditions under which an invariance property holds for the class of selection distributions. First, we consider
selection distributions arising from two uncorrelated random vectors. In that setting, the invariance holds for the so-called
C{\cal{C}} -class and for elliptical distributions. Second, we describe the invariance property for selection distributions arising
from two correlated random vectors. The particular case of the distribution of quadratic forms and its invariance, under various
selection distributions, is investigated in more details. We describe the application of our invariance results to sample
variogram and covariogram estimators used in spatial statistics and provide a small simulation study for illustration. We
end with a discussion about other applications, for example such as linear models and indices of temporal/spatial dependence. 相似文献
7.
A weighted weak invariance principle for nonseparable Banach space-valued functions is described via asymptotic behavior of a weighted Wiener process. It is proved that, unlike the usual weak invariance principle, the weighted variant cannot be characterized via validity of a central limit theorem in a Banach space. A strong invariance principle is introduced in the present context and used to prove the weighted weak invariance principle that we seek herewith. The result then is applied to empirical processes. 相似文献
8.
强不变原理与完全收敛性的统一形式 总被引:1,自引:0,他引:1
本文建立了强不变原理与完全收效性的统一形式,得到了用强不变原理研究完全收敛性的方法,前人许多关于强不交原理和完全收敛性的结论是本文的推论. 相似文献
9.
This paper studies conditions for invariance of dynamical systems on stratified domains as originally introduced by Bressan and Hong. We establish Hamiltonian conditions for both weak and strong invariance of trajectories on systems with non-Lipschitz data. This is done via the identification of a new multifunction, the essential velocity multifunction. Properties of this multifunction are investigated and used to establish the relevant invariance criteria. 相似文献
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《中国科学 数学(英文版)》2015,(6)
We obtain a general invariance principle of G-Brownian motion for the law of the iterated logarithm(LIL for short). For continuous bounded independent and identically distributed random variables in G-expectation space, we also give an invariance principle for LIL. In some sense, this result is an extension of the classical Strassen's invariance principle to the case where probability measure is no longer additive. Furthermore,we give some examples as applications. 相似文献
13.
The objective of this paper is to consider shift invariance, a specific type of exchangeability, of random factors in linearmodels.
The randomfactors are described via their covariance matrices and it is shown that shift invariance implies circular Toeplitz
covariancematrices and marginally shift invariance implies block circular Toeplitz covariance matrices. In order to get interpretable
linear models reparametrization is performed. It is shown that by putting restrictions on the spectrum of the shift invariant
covariance matrices natural reparametrization conditions for the corresponding factors are obtained which then, among others,
can be used to obtain unique parametrizations under shift invariance.
相似文献
14.
Tian Chou 《数学年刊B辑(英文版)》1994,15(2):241-246
ANINVARIANCEOFCDFEQUATION¥TIANCHOUAbstract:ThispaperpresentsanewinvariancefortheCDFequation.Usingthisinvariance,theauthorobta... 相似文献
15.
The invariance principles for autonomous difference systems with infinite delay are established.As applications of the obtained invariance principles, criteria for asymptotic stability and asymptotic constancy of solutions are also given. 相似文献
16.
《随机分析与应用》2013,31(5):955-981
Abstract Thanks to the Stroock and Varadhan “Support Theorem” and under convenient regularity assumptions, stochastic viability problems are equivalent to invariance problems for control systems (also called tychastic viability), as it has been singled out by Doss in 1977 for instance. By the way, it is in this framework of invariance under control systems that problems of stochastic viability in mathematical finance are studied. The Invariance Theorem for control systems characterizes invariance through first‐order tangential and/or normal conditions whereas the stochastic invariance theorem characterizes invariance under second‐order tangential conditions. Doss's Theorem states that these first‐order normal conditions are equivalent to second‐order normal conditions that we expect for invariance under stochastic differential equations for smooth subsets. We extend this result to any subset by defining in an adequate way the concept of contingent curvature of a set and contingent epi‐Hessian of a function, related to the contingent curvature of its epigraph. This allows us to go one step further by characterizing functions the epigraphs of which are invariant under systems of stochastic differential equations. We shall show that they are (generalized) solutions to either a system of first‐order Hamilton‐Jacobi equations or to an equivalent system of second‐order Hamilton‐Jacobi equations. 相似文献
17.
We show that there exists an ergodic conductance environment such that the weak (annealed) invariance principle holds for the corresponding continuous time random walk but the quenched invariance principle does not hold. 相似文献
18.
相对论Birkhoff系统的形式不变性与Noether守恒量 总被引:2,自引:0,他引:2
研究相对论Birkhoff系统的形式不变性,寻求系统的守恒量。在群的无限小变换下,给出相对论Birkhoff系统的形式不变性的定义和判剧。基于相对论Pfaff-Birkhoff-D'Alembert原理在群的无限小变换下的变形形式,建立相对论Birkhoff系统的Noether对称性理论。通过研究形式不变性与Noether对称性之间的关系,得到相对论Birkhoff系统的守恒量。研究结果表明:在一定的条件下,相对论Birkhoff系统的形式不变性导致Noether对称性的守恒量。 相似文献
19.
Uwe Einmahl 《Probability Theory and Related Fields》1987,76(1):81-101
Summary An estimate of the convergence speed in the multidimensional invariance principle is obtained. Using this estimate, we can
prove strong invariance principles for partial sums of independent not necessarily identically distributed multidimensional
random vectors. 相似文献
20.
Guy Martial Nkiet 《Journal of multivariate analysis》2003,84(1):1-18
Using a recent result about the invariance problem in linear canonical analysis (LCA), we introduce a criterion by means of which one can see if this invariance holds when the related random vectors are transformed by linear maps. Then, the estimation of this criterion is considered as well as the problem of testing for invariance of LCA. Particularly, a new test for additional information in canonical analysis is proposed and simulations are used to gain understanding of the finite sample performance of this test and to compare it with the likelihood ratio test. 相似文献