共查询到20条相似文献,搜索用时 15 毫秒
1.
W. J. Park 《Journal of multivariate analysis》1974,4(4):479-485
Strassen's version of the law of the iterated logarithm is extended to the two-parameter Gaussian process {X(s, t); ε(s, t) [0, ∞)2} with the covariance function R((s1,t1),(s2,t2)) = min(s1,s2)min(t1,t2). 相似文献
2.
The recent interest in iterated Wiener processes was motivated by apparently quite unrelated studies in probability theory and mathematical statistics. Laws of the iterated logarithm (LIL) were independently obtained by Burdzy(2) and Révész(17). In this work, we present a functional version of LIL for a standard iterated Wiener process, in the spirit of functional asymptotic results of an 2-valued Gaussian process given by Deheuvels and Mason(9) in view of Bahadur-Kiefer-type theorems. Chung's liminf sup LIL is established as well, thus providing further insight into the asymptotic behavior of iterated Wiener processes. 相似文献
3.
Hå kan Hedenmalm Ilgiz Kayumov 《Proceedings of the American Mathematical Society》2007,135(7):2235-2248
We obtain considerable improvement of Makarov's estimate of the boundary behavior of a general conformal mapping from the unit disk to a simply connected domain in the complex plane. We apply the result to improve Makarov's comparison of harmonic measure with Hausdorff measure on simply connected domains.
4.
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
5.
蒋烨 《高校应用数学学报(英文版)》2003,18(2):200-208
§ 1 IntroductionA finite family of random variables { Xi,1≤ i≤ n} is said to be negatively associated(NA) is for every pair of disjointsubsets A1 and A2 of{ 1 ,2 ,...,n} ,Cov{ f1 (Xi,i∈ A1 ) ,f2 (Xj,j∈ A2 ) }≤ 0 ,(1 .1 )whenever f1 and f2 are coordinatewise increasing and the covariance exists.An infinitefamily is negatively associated ifevery finite subfamily is negatively associated.This defini-tion was introduced by Alam and Saxena[1 ] and Joag-Dev and Proschan[2 ] .As pointed… 相似文献
6.
Jürg Hüsler 《Journal of multivariate analysis》1981,11(2):273-279
Let {Xn, n ≥ 1} be a real-valued stationary Gaussian sequence with mean zero and variance one. Let Mn = max{Xt, i ≤ n} and Hn(t) = (M[nt] ? bn)an?1 be the maximum resp. the properly normalised maximum process, where , and . We characterize the almost sure limit functions of (Hn)n≥3 in the set of non-negative, non-decreasing, right-continuous, real-valued functions on (0, ∞), if r(n) (log n)3?Δ = O(1) for all Δ > 0 or if r(n) (log n)2?Δ = O(1) for all Δ > 0 and r(n) convex and fulfills another regularity condition, where r(n) is the correlation function of the Gaussian sequence. 相似文献
7.
AndréRobert Dabrowski 《Statistics & probability letters》1985,3(4):209-212
Recently, a functional central limit theorem and a Berry-Essen Theorem have been demonstrated for classes or associated random variables. Using these results, and similar results for multiplicative sequences, we show a functional law of the iterated logarithm for associated sequences satisfying a rate requirement. 相似文献
8.
Let {β(s), s ≥ 0} be the standard Brownian motion in ℝ
d
with d ≥ 4 and let |W
r
(t)| be the volume of the Wiener sausage associated with {β(s), s ≥ 0} observed until time t. From the central limit theorem of Wiener sausage, we know that when d ≥ 4 the limit distribution is normal. In this paper, we study the laws of the iterated logarithm for
| Wr (t) | - \mathbbE| Wr (t) |\left| {W_r (t)} \right| - \mathbb{E}\left| {W_r (t)} \right| in this case. 相似文献
9.
J. Norkūunienė 《Lithuanian Mathematical Journal》2006,46(4):432-445
The strong convergence of dependent random variables is analyzed and the law of iterated logarithm for real additive functions
defined on the class
of combinatorial assemblies is obtained.
Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 532–547, October–December, 2006. 相似文献
10.
K. Fukuyama 《Acta Mathematica Hungarica》2008,118(1-2):155-170
It is proved that two types of discrepancies of the sequence {θ
n
x} obey the law of the iterated logarithm with the same constant. The appearing constants are calculated explicitly for most
of θ > 1.
Dedicated to the memory of Professor Walter Philipp 相似文献
11.
Miguel A. Arcones 《Journal of Theoretical Probability》1995,8(2):433-451
The compact law of the iterated logarithm for empirical processes whose underlying sequence satisfies a -mixing condition is considered. In particular, we show a compact law of the iterated logarithm for VC subgraph classes of functions, for classes of functions which satisfy the bracketing condition in Doukhanet al.
(6) and for some classes of smooth functions.Research partially supported by NSF Grant DMS-93-02583. 相似文献
12.
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
13.
In this paper, we investigate functional limit problem for path of a Brownian sheet, Chung's functional law of the iterated logarithm for a Brownian sheet is obtained. The main tool in the proof is large deviation and small deviation for a Brownian sheet. 相似文献
14.
Wel Dong LIU Zheng Yan LIN 《数学学报(英文版)》2008,24(1):59-74
Let {X, X1, X2,...} be a strictly stationaryφ-mixing sequence which satisfies EX = 0,EX^2(log2{X})^2〈∞and φ(n)=O(1/log n)^Tfor some T〉2.Let Sn=∑k=1^nXk and an=O(√n/(log2n)^γ for some γ〉1/2.We prove that limε→√2√ε^2-2∑n=3^∞1/nP(|Sn|≥ε√ESn^2log2n+an)=√2.The results of Gut and Spataru (2000) are special cases of ours. 相似文献
15.
汪嘉冈 《应用数学学报(英文版)》1994,10(1):59-68
ALAWOFTHEITERATEDLOGARITHMFORPROCESSESWITHINDEPENDENTINCREMENTSWANGJIAGANG(汪嘉冈)(EastChinaUniversityofScience&Technology,Shang... 相似文献
16.
Hwai-Chung Ho 《Journal of Theoretical Probability》1995,8(2):347-360
It is shown in the present paper that the upper-half law of the iterated logarithm with the usual norming rate
still holds for certain class of non-instantaneous filters of strongly dependent Gaussian sequences. 相似文献
17.
Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q(n)be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q(n)≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t≤1B(t)-inf0≤t≤sB(t),and B(t) is a Brownian bridge. 相似文献
18.
Small ball probabilities are estimated for Gaussian processes with stationary increments when the small balls are given by various Hölder norms. As an application we establish results related to Chung's functional law of the iterated logarithm for fractional Brownian motion under Hölder norms. In particular, we identify the points approached slowest in the functional law of the iterated logarithm.Supported in part by NSF Grant DMS-9024961. 相似文献
19.
Fu Qing Gao 《数学学报(英文版)》2009,25(2):209-222
Three types of laws of the iterated logarithm (LIL) for locally square integrable martingales with continuous parameter are considered by a discretization approach. By this approach, a lower bound of LIL and a number of FLIL are obtained, and Chung LIL is extended. 相似文献
20.
Terence Chan 《Journal of Theoretical Probability》1995,8(3):643-667
For 0<<1, let
. The questions addressed in this paper are motivated by a result due to Strassen: almost surely, lim sup
t
U
((t))=1–exp{–4(–1)–1}. We show that Strassen's result is closely related to a large deviations principle for the family of random variablesU
(t), t>0. Also, when =1,U
(t)0 almost surely and we obtain some bounds on the rate of convergence. Finally, we prove an analogous limit theorem for discounted averages of the form
as 0, whereD is a suitable discount function. These results also hold for symmetric random walks. 相似文献