共查询到20条相似文献,搜索用时 156 毫秒
1.
Philippe Berthet Mikhail Lifshits 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2002,38(6):811
We find exact convergence rate in the Strassen's functional law of the iterated logarithm for a class of elements on the boundary of the limit set. Our result applies, in particular, to the power functions cαxα with α ]1/2,1[, thus solving a small ball estimate problem which was open for ten years. 相似文献
2.
Miguel A. Arcones 《Journal of Theoretical Probability》1999,12(3):615-641
Let {X
j
}
j = 1
be a stationary Gaussian sequence of random vectors with mean zero. We give sufficient conditions for the compact law of the iterate logarithm of
where G is a real function defined on
d
with finite second moment. Our result builds on Ho,(6) who proved an upper-half of the law of iterated logarithm for a sequence of random variables. 相似文献
3.
Law of the iterated logarithm for transitiveC
2 Anosov flows and semiflows over maps of the interval
Sherman Wong 《Monatshefte für Mathematik》1982,94(2):163-173
It is proved that a functional law of the iterated logarithm is valid for transitiveC
2 Anosov flows on compact Riemannian manifolds when the observable belongs to a certain class of real-valued Hölder functions. The result is equally valid for semiflows over piecewise expanding interval maps that are similar to the Williams' Lorenz-attractor semiflows. Furthermore the observables need only be real-valued Hölder for these semiflows. 相似文献
4.
Michael Lacey 《Journal of Theoretical Probability》1989,2(3):377-398
We establish a bounded and a compact law of the iterated logarithm for partial sum processes indexed by classes of functions. We assume a growth condition on the metric entropy under bracketing. Examples show that our results are sharp. As a corollary we obtain new results for weighted sums of independent identically distributed random variables. 相似文献
5.
A. N. Frolov 《Journal of Mathematical Sciences》2005,128(1):2614-2624
We study the almost sure behavior of increments of renewal processes. We derive a universal form of norming functions in the strong limit theorems for increments of such processes. This result unifies the following well-known theorems for increments of renewal processes: the strong law of large numbers, Erdos-Renyi law, Csorgo-Revesz law, and law of the iterated logarithm. New results are obtained for processes with distributions of renewal times from domains of attraction of the normal law and completely asymmetric stable laws with index (1, 2). Bibliography: 15 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 298, 2003, pp. 208–225. 相似文献
6.
Let
be the Poisson point process with intensity 1 in [–n,n]
d
. We prove the law of the iterated logarithm for the total length of the nearest neighbor graph on
. 相似文献
7.
In this paper we show that the closure of the space BMOA of analytic functions of bounded mean oscillation in the Bloch spaceB is the image P(U) of space of all continuous functions on the maximal ideal space ofH
under the Bergman projection P. It is proved that the radial growth of functions in P(U) is slower than the iterated logarithm studied by Makarov. So some geometric conditions are given for functions in P(U), which we can easily use to construct many Bloch functions not in P(U). 相似文献
8.
Gregory J. Morrow 《Probability Theory and Related Fields》1981,57(2):265-291
Summary Given independent identically distributed random variables {x
n
;n
q
| indexed by q-tuples of positive integers and taking values in a separable Banach space B we approximate the rectangular sums
by a Brownian sheet. We obtain the corresponding result for random variables with values in a separable Hilbert space H while assuming an optimal moment condition. Generalized versions of the functional law of the iterated logarithm are thus derived. 相似文献
9.
O. Sh. Sharipov 《Lithuanian Mathematical Journal》2009,49(2):203-215
Under optimal moment conditions, we prove the compact law of the iterated logarithm and the almost sure invariance principle
for ψ-mixing random variables with values in type 2 Banach spaces. These results, together with the bounded law of the iterated
logarithm proved earlier by author, allow us to prove the same kind of results for the Banach space valued autoregressive
processes with ψ-mixing innovations. The results for autoregressive processes can be considered as asymptotic properties of the estimator
of mean. 相似文献
10.
V. V. Petrov 《Vestnik St. Petersburg University: Mathematics》2017,50(1):32-34
Sufficient conditions for the applicability of the law of the iterated logarithm to sequences of dependent random variables are obtained. As a corollary, a theorem on the law of the iterated logarithm for a sequence of m-orthogonal random variables is proved. 相似文献
11.
Z. Shi 《Journal of Theoretical Probability》1996,9(4):915-929
LetR be the radial part of ad-dimensional Wiener process, starting from 0. In this paper, small ball probabilities are evaluated for sup0<11(t
–p
R(t)) and sup
t
0(e
–1
R(t)), withp[0, 1/2]. Chung's law of the iterated logarithm is established for the supremum of the local times of a two-dimensional Bessel process. 相似文献
12.
Xiaojing Xiang 《Annals of the Institute of Statistical Mathematics》1995,47(1):105-117
A necessary condition for the asymptotic normality of the sample quantile estimator isf(Q(p))=F(Q(p))>0, whereQ(p) is thep-th quantile of the distribution functionF(x). In this paper, we estimate a quantile by a kernel quantile estimator when this condition is violated. We have shown that the kernel quantile estimator is asymptotically normal in some nonstandard cases. The optimal convergence rate of the mean squared error for the kernel estimator is obtained with respect to the asymptotically optimal bandwidth. A law of the iterated logarithm is also established.This research was partially supported by the new faculty award from the University of Oregon. 相似文献
13.
We consider perturbed empirical distribution functions
, where {Ginn, n1} is a sequence of continuous distribution functions converging weakly to the distribution function of unit mass at 0, and {X
i, i1} is a non-stationary sequence of absolutely regular random variables. We derive the almost sure representation and the law of the iterated logarithm for the statistic
whereU
n
is aU-statistic based onX
1,...,X
n
. The results obtained extend or generalize the results of Nadaraya,(7) Winter,(16) Puri and Ralescu,(9,10) Oodaira and Yoshihara,(8) and Yoshihara,(19) among others.Research supported by the Office of Naval Research Contract N00014-91-J-1020. 相似文献
14.
V. O. Koval’ 《Ukrainian Mathematical Journal》2006,58(7):1139-1143
We investigate a bounded law of the iterated logarithm for matrix-normalized weighted sums of martingale differences in R
d
. We consider the normalization of matrices inverse to the covariance matrices of these sums by square roots. This result
is used for the proof of the bounded law of the iterated logarithm for martingales with arbitrary matrix normalization.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 7, pp. 1006–1008, July, 2006. 相似文献
15.
A. N. Frolov 《Journal of Mathematical Sciences》2005,128(1):2604-2613
We derive universal strong laws for increments of sums of i.i.d. random variables with multidimensional indices without an exponential moment. Our theorems yield the strong law of large numbers, the law of the iterated logarithm, and the Csorgo-Revesz laws for random fields. New results are obtained for distributions from domains of attraction of the normal law and of completely asymmetric stable laws with index (1, 2). Bibliography: 18 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 298, 2003, pp. 191–207. 相似文献
16.
《随机分析与应用》2013,31(1):181-203
Abstract We consider a sequence (Z n ) n≥1 defined by a general multivariate stochastic approximation algorithm and assume that (Z n ) converges to a solution z* almost surely. We establish the compact law of the iterated logarithm for Z n by proving that, with probability one, the limit set of the sequence (Z n ? z*) suitably normalized is an ellipsoid. We also give the law of the iterated logarithm for the l p norms, p ∈ [1, ∞], of (Z n ? z*). 相似文献
17.
吴黎明 《应用数学学报(英文版)》2000,16(2):149-161
1.IntroductionandMainResultsAssumethat(Xt),.T(T~NorAl)isaPolishspaceE-valuedMarkovprocess,definedon(fi,F,(R),(ot),(P-c)..E),withitssemigroupoftransitionkernels(Pt).Here(ot)isthesemigroupofshiftsonfisuchthatX.(otw)~X. t(w),Vs,tET;(R)isthenaturalfiltration.Throughoutthispaperweassumethat(Pt)issymmetricandergodicwithrespectto(w.r.t.forshort)aprobabilitymeasurepon(E,e)(eistheBorela--fieldofE),i.e.,.Symmetry:(Ptf,g)~(f,Pig):~isfptgdp,acET,if,gCL'(P);.ErgodicitytFOranyfEL'(P),ifPtf~f… 相似文献
18.
H. -P. Scheffler 《Journal of Mathematical Sciences》1998,89(5):1545-1552
Let X1, X2, ... be a sequence of independent and identically distributed (i.i.d.)R
d-valued random vectors distributed according to a full (B,c) semistable law without Gaussian component. Then the following
law of the iterated logarithm holds.
This result is new even in the one-dimensional situation of semistable laws on the real line, where we extend our result
to laws in the domain of normal attraction of a semistable law. Furthermore, we prove that this kind of law of the iterated
logarithm also holds for certain semistable laws on homogeneous groups, especially on Heisenberg groups.
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I. 相似文献
19.
L. Olsen 《Indagationes Mathematicae》2006,17(1):85-102
We study the exact rate of convergence of frequencies of digits of “normal” points of a self-similar set. Our results have applications to metric number theory. One particular application gives the following surprising result: there is an uncountable family of pairwise disjoint and exceptionally big subsets of ?d that do not obey the law of the iterated logarithm. More precisely, we prove that there is an uncountable family of pairwise disjoint and exceptionally big sets of points x in ?d—namely, sets with full Hausdorff dimension—for which the rate of convergence of frequencies of digits in the N-adic expansion of x is either significantly faster or significantly slower than the typical rate of convergence predicted by the law of the iterated logarithm. 相似文献
20.
We prove a conjecture of Zahariuta which itself solves a problem of Kolmogorov on the -entropy of some classes of analytic functions. For a given holomorphically convex compact subset K in a pseudoconvex domain D in Cn, Zahariutas conjecture consists in approximating the relative extremal function u*K,D, uniformly on any compact subset of DK, by pluricomplex Green functions on D with logarithmic poles in the compact subset K. 相似文献