共查询到20条相似文献,搜索用时 31 毫秒
1.
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
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.
U. Einmahl 《Journal of Mathematical Sciences》2009,163(4):311-327
We provide a strong invariance principle for sums of independent, identically distributed random vectors that need not have
finite second absolute moments. Various applications are indicated. In particular, we show how one can re-obtain some recent
LIL type results from this invariance principle. Bibliography: 16 titles. 相似文献
4.
《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
5.
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.
6.
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
7.
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
8.
In this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed(IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's central limit theorem and invariance principle to the case where probability measures are no longer additive. 相似文献
9.
Yuri Kifer 《Journal of Theoretical Probability》2013,26(2):489-513
In Kifer and Varadhan (Ann Probab, to appear), we obtained a nonconventional invariance principle (functional central limit theorem) for sufficiently fast mixing stochastic processes with discrete and continuous time. In this article, we derive a nonconventional invariance principle for sufficiently well-mixing random fields. 相似文献
10.
An invariance principle for semimartingale reflecting Brownian motions in an orthant 总被引:1,自引:0,他引:1
Semimartingale reflecting Brownian motions in an orthant (SRBMs) are of interest in applied probability because of their role
as heavy traffic approximations for open queueing networks. It is shown in this paper that a process which satisfies the definition
of an SRBM, except that small random perturbations in the defining conditions are allowed, is close in distribution to an
SRBM. This perturbation result is called an invariance principle by analogy with the invariance principle of Stroock and Varadhan
for diffusions with boundary conditions. A crucial ingredient in the proof of this result is an oscillation inequality for
solutions of a perturbed Skorokhod problem. In a subsequent paper, the invariance principle is used to give general conditions
under which a heavy traffic limit theorem holds for open multiclass queueing networks.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
11.
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
12.
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
13.
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
14.
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
15.
《Statistics & probability letters》1988,7(1):23-26
We prove strong invariance principles for exchangeable sequences of real random variables. Under the same conditions as those used for the central limit theorem, we obtain Strassen's invariance principle. 相似文献
16.
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
17.
It is proved that a general governing relationship results for an inhomogeneously ageing hereditary medium under fairly broad assumptions from the principle of material independence from the reference system /1/, also later called the principle of invariance. 相似文献
18.
《Journal of Applied Mathematics and Mechanics》1998,62(1):95-102
Issues on attraction in autonomous mechanical systems with ideal holonomic bilateral constraints acted upon by potential gyroscopic dissipative forces and forces of sliding friction are considered. In particular, the semi-invariance of ω-limit sets and the conditions for the dichotomy of such systems are established. The investigation is based on the invariance principle using several Lyapunov functions, combining the methods of [1] with the La Salle invariance principle [2, 3] applied to autonomous systems with a discontinuous right-hand side. 相似文献
19.
Summary A general class of statistics based on sequential ranks is introduced. Under suitable regularity conditions, an almost sure representation and invariance principle are established for this class. In particular, it is shown that these statistics can obey invariance principles that are radically different from those obeyed by the usual full rank statistics.Research supported by the CSIR and the University of South AfricaResearch supported by the University of Delaware Research Foundation, Grant #8325530015 相似文献
20.
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