共查询到20条相似文献,搜索用时 31 毫秒
1.
J Kuelbs 《Journal of multivariate analysis》1973,3(2):161-172
We extend the invariance principle to triangular arrays of Banach space valued random variables, and as an application derive the invariance principle for lattices of random variables. We also point out how the q-dimensional time parameter Yeh-Wiener process is naturally related to a one dimensional time Wiener process with an infinite dimensional Banach space as a state space. 相似文献
2.
André Dabrowski Herold Dehling Walter Philipp 《Probability Theory and Related Fields》1984,65(4):483-491
Summary We give a simpler proof of the probability invariance principle for triangular arrays of independent identically distributed random variables with values in a separable Banach space, recently proved by de Acosta [1], and improve this result to an almost sure invariance principle. 相似文献
3.
Several concepts for the localization of a frame are studied. The
intrinsic localization of a frame is defined by the decay properties
of its Gramian matrix. Our main result asserts that the canonical
dual frame possesses the same intrinsic localization as the original
frame. The proof relies heavily on Banach algebra techniques, in
particular on recent spectral invariance properties for certain
Banach algebras of infinite matrices. Intrinsically localized frames extend in a natural way to Banach frames for a class of associated Banach spaces which are defined by
weighted ℓp-coefficients of their frame expansions. As an
example, the time--frequency concentration of distributions is
characterized by means of localized (nonuniform) Gabor frames. 相似文献
4.
In this paper, we reveal several basic properties about nonlinear vector-valued weighted pseudo almost automorphic functions, including equivalence, completeness, translation invariance, composition theorem, and convolution theorem of these functions. We also give some concrete examples to illustrate our results. Finally, we obtain a new existence theorem of nonlinear weighted pseudo almost automorphic solutions for semilinear evolution equations in Banach spaces. 相似文献
5.
Ernst Eberlein 《Probability Theory and Related Fields》1979,50(2):119-133
Summary It is shown that for -mixing arrays of Banach space valued random vectors the central limit theorem implies the invariance principle. Applying this result to lattices of random variables a higher dimensional invariance principle under dependence assumptions is obtained.Dedicated to Professor Leopold Schmetterer 相似文献
6.
吴群英 《数学年刊A辑(中文版)》2014,35(2):225-234
考虑独立但不同分布的正随机变量序列,建立了关于部分和乘积的弱不变原理的一个普遍性结果,推广和改进了由Matula和Stepien在2009年以及Rempala和Wesolowski在2002年获得的弱不变原理. 相似文献
7.
We study several aspects of a generalized Perron-Frobenius and Krein-Rutman theorems concerning spectral properties of a (possibly unbounded) linear operator on a cone in a Banach space. The operator is subject to the so-called tangency or weak range assumptions implying the resolvent invariance of the cone. The further assumptions rely on relations between the spectral and essential spectral bounds of the operator. In general we do not assume that the cone induces the Banach lattice structure into the underlying space. 相似文献
8.
Youhe Feng 《Mathematical Methods in the Applied Sciences》1996,19(11):847-856
Using the invariance principle in a Banach space with less restriction, we discuss the asymptotic behaviour of an integro-differential equation with infinite delay which is an infection disease model. It is proved that the equilibria are globally asymptotic stable if the parameters fit some relation and the integral kern satisfies a convergence condition. 相似文献
9.
P.N. Dowling D. Freeman C.J. Lennard E. Odell B. Randrianantoanina B. Turett 《Journal of Functional Analysis》2012,263(5):1378-1381
The Grothendieck compactness principle states that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. In this article, an analogue of the Grothendieck compactness principle is considered when the norm topology of a Banach space is replaced by its weak topology. It is shown that every weakly compact subset of a Banach space is contained in the closed convex hull of a weakly null sequence if and only if the Banach space has the Schur property. 相似文献
10.
11.
We prove a strong invariance principle for the two-parameter empirical process of stationary sequences under a new weak dependence assumption. We give several applications of our results. 相似文献
12.
New Sobolev type embeddings for some weighted Banach spaces are established. Using such embeddings and the singular positive radial entire solutions, we construct singular positive weak solutions with a prescribed singular set for a weighted elliptic equation. Our main results in this paper also provide positive weak solutions with a prescribed singular set to an equation with Hardy potential. 相似文献
13.
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
14.
In this paper we begin the study of some important Banach spaces of slice hyperholomorphic functions, namely the Bloch, Besov and weighted Bergman spaces, and we also consider the Dirichlet space, which is a Hilbert space. The importance of these spaces is well known, and thus their study in the framework of slice hyperholomorphic functions is relevant, especially in view of the fact that this class of functions has recently found several applications in operator theory and in Schur analysis. We also discuss the property of invariance of these function spaces with respect to Möbius maps by using a suitable notion of composition. 相似文献
15.
Cylindrical Wiener processes in real separable Banach spaces are defined, and an approximation theorem involving scalar Wiener processes is given for such processes. A weak stochastic integral for Banach spaces involving a cylindrical Wiener process as integrator and an operator-valued stochastic process as integrand is defined. Basic properties of this integral are stated and proved.A class of linear, time-invariant, stochastic differential equations in real, separable, reflexive Banach spaces is formulated in such fashion that a solution of the equation is a cylindrical process. An existence and uniqueness theorem is proved. A stochastic version of the problem of heat conduction in a ring provides an example.Research supported by National Science Foundation under Grant No. ECS-8005960. 相似文献
16.
Jürgen Dippon 《随机分析与应用》2013,31(5):765-798
Parallelization of stochastic approximation procedures can reduce computation and total observation time of a system. Concerning the number of all observations used by the pure sequential and the suggested parallel method a weak invariance principle implies the asymptotic equivalence of both methods. A loglog invariance principle and a rate of a.s. convergence result describe the pathwise properties. Due to the parallel design asymptotic confidence regions can readily be constructed either by computing the bootstrap distribution or the Gaussian limit distribution determined by the empirical covariance 相似文献
17.
Ioannis K. Argyros 《Journal of Applied Mathematics and Computing》1997,4(2):263-280
In this study we prove the mesh-independence principle via Steffensen’s method. This principle asserts that when Steffensen’s method is applied to a nonlinear equation between some Banach spaces, as well as to some finite-dimensional discretization of that equation, then the behavior of the discretized process is asymptotically the same as that for the original iteration. Local and semilocal convergence results as well as an error analysis for Steffensen’s method are also provided. 相似文献
18.
C. P. Walkden 《Transactions of the American Mathematical Society》2007,359(3):1081-1097
We consider iterated function schemes that contract on average. Using a transfer operator approach, we prove a version of the almost sure invariance principle. This allows the system to be modelled by a Brownian motion, up to some error term. It follows that many classical statistical properties hold for such systems, such as the weak invariance principle and the law of the iterated logarithm.
19.
Yuri Borovskikh 《Acta Appl Math》1994,35(3):213-298
U-statistics in Banach spaces are considered and thoroughly investigated. The martingale structure, estimates of moments, the law of large numbers, the central limit theorem, the invariance principle, estimates of the rate of convergence, and large deviations are established 相似文献
20.
Invariance principles for sums of Banach space valued random elements and empirical processes 总被引:5,自引:0,他引:5
Summary Almost sure and probability invariance principles are established for sums of independent not necessarily measurable random elements with values in a not necessarily separable Banach space. It is then shown that empirical processes readily fit into this general framework. Thus we bypass the problems of measurability and topology characteristic for the previous theory of weak convergence of empirical processes.Both authors were partially supported by NSF grants. This work was done while the second author was visiting the M.I.T. Mathematics Department 相似文献