共查询到20条相似文献,搜索用时 15 毫秒
1.
H. Walk 《Archiv der Mathematik》2007,89(5):466-480
For a sequence of real random variables C
α-summability is shown under conditions on the variances of weighted sums, comprehending and sharpening strong laws of large
numbers (SLLN) of Rademacher-Menchoff and Cramér-Leadbetter, respectively. Further an analogue of Kolmogorov’s criterion for
the SLNN is established for E
α-summability under moment and multiplicativity conditions of 4th order, which allows one to weaken Chow’s independence assumption
for identically distributed square integrable random variables. The simple tool is a composition of Cesàro-type and of Euler
summability methods, respectively.
Received: 12 June 2006, Revised: 14 May 2007 相似文献
2.
B.G. Pittel 《Stochastic Processes and their Applications》1980,10(1):33-48
Let X1,X2,… be i.i.d. random variables with a continuous distribution function. Let R0=0, Rk=min{j>Rk?1, such that Xj>Xj+1}, k?1. We prove that all finite-dimensional distributions of a process , converge to those of the standard Brownian motion. 相似文献
3.
P. Révész 《Stochastic Processes and their Applications》1983,15(2):169-179
Let U1, U2,… be a sequence of independent, uniform (0, 1) r.v.'s and let R1, R2,… be the lengths of increasing runs of {Ui}, i.e., X1=R1=inf{i:Ui+1<Ui},…, Xn=R1+R2+?+Rn=inf{i:i>Xn?1,Ui+1<Ui}. The first theorem states that the sequence can be approximated by a Wiener process in strong sense.Let τ(n) be the largest integer for which R1+R2+?+Rτ(n)?n, and . Here Mn is the length of the longest increasing block. A strong theorem is given to characterize the limit behaviour of Mn.The limit distribution of the lengths of increasing runs is our third problem. 相似文献
4.
Let Ωm be the set of partitions, ω, of a finite m-element set; induce a uniform probability distribution on Ωm, and define Xms(ω) as the number of s-element subsets in ω. We alow the existence of an integer-valued function n=n(m)(t), t?[0, 1], and centering constants bms, 0?s? m, such that converges to the ‘Brownian Bridge’ process in terms of its finite-dimensional distributions. 相似文献
5.
G. Hurelbaatar 《Periodica Mathematica Hungarica》1995,31(3):189-200
LetS
n be the partial sums of -mixing stationary random variables and letf(x) be a real function. In this note we give sufficient conditions under which the logarithmic average off(S
n
/
n
) converges almost surely to
–
f(x)d(x). We also obtain strong approximation forH(n)=
k=1
n
k
–1
f(S
k
/k)=logn
–
f(x)d(x) which will imply the asymptotic normality ofH(n)/log1/2
n. But for partial sums of i.i.d. random variables our results will be proved under weaker moment condition than assumed for -mixing random variables. 相似文献
6.
J. E. Yukich 《Probability Theory and Related Fields》1995,102(2):203-220
Summary LetU
1,...,Un denote i.i.d. random variables with the uniform distribution on [0, 1]2, and letT
2T2(U1,...,Un) denote the shortest tour throughU
1,...,Un with square-weighted edges. By drawing on the quasi-additive structure ofT
2 and the boundary rooted dual process, it is shown that lim
n
E
T
2(U
1,...,Un)= for some finite constant .This work was supported in part by NSF Grant DMS-9200656, Swiss National Foundation Grant 21-298333.90, and the US Army Research Office through the Mathematical Sciences Institute of Cornell University, whose assistance is gratefully acknowledged 相似文献
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12.
Min-Young Lee 《Aequationes Mathematicae》1992,44(2-3):220-225
Summary LetA
1,A
2, ,A
m
,C
1,C
2, ,C
n
be events on a given probability speace. LetV
m
andU
n
, respectively, be the numbers among theA
i
's andC
j
's which occur.Upper and lower bounds ofP(V
m
1, U
n
1) are obtained by means of the bivariate binomial moments. These extend recent univariate optimal Bonferroni-type inequalities. 相似文献
13.
It is known that a branching process in a random environment (BPRE) which is subcritical or critical either dies with probability one or, in the trivial case, corresponds to an immortal sterile population. In the supercritical case, various conditions are known to be necessary for noncertain extinction while other conditions are known to be sufficient. In this paper, a necessary and sufficient condition for noncertain extinction of a supercritical BPRE is given. In particular, it is shown that a supercritical BPRE has noncertain extinction if and only if there exists a random truncation, depending only on the environmental sequence, such that the truncated BPRE is supercritical and such that the sequence of truncation points grows more slowly than any exponential sequence. 相似文献
14.
David Tanny 《Stochastic Processes and their Applications》1978,6(2):201-211
Normalizing constants are obtained for B.P.R.E. such that the limiting random variable is finite almost everywhere and is zero only on the extinction set of the process w.p.1. Furthermore, the normalizing constants can be chosen so that they grow exponentially fast, and so that the ratio of successive constants converges in distribution. The method of proof used is to prove the result for increasing branching processes, and then, to transfer the result to general B.P.R.E. by employing the relationships between B.P.R.E., the associated B.P.R.E., and the reduced branching process. 相似文献
15.
K. F. Cheng 《Annals of the Institute of Statistical Mathematics》1982,34(1):479-489
Summary Letf
n
(p)
be a recursive kernel estimate off
(p) thepth order derivative of the probability density functionf, based on a random sample of sizen. In this paper, we provide bounds for the moments of
and show that the rate of almost sure convergence of
to zero isO(n
−α), α<(r−p)/(2r+1), iff
(r),r>p≧0, is a continuousL
2(−∞, ∞) function. Similar rate-factor is also obtained for the almost sure convergence of
to zero under different conditions onf.
This work was supported in part by the Research Foundation of SUNY. 相似文献
16.
Eric M. Rains 《Probability Theory and Related Fields》1998,112(3):411-423
Using the machinery of zonal polynomials, we examine the limiting behavior of random symmetric matrices invariant under conjugation
by orthogonal matrices as the dimension tends to infinity. In particular, we give sufficient conditions for the distribution
of a fixed submatrix to tend to a normal distribution. We also consider the problem of when the sequence of partial sums of
the diagonal elements tends to a Brownian motion. Using these results, we show that if O
n
is a uniform random n×n orthogonal matrix, then for any fixed k>0, the sequence of partial sums of the diagonal of O
k
n
tends to a Brownian motion as n→∞.
Received: 3 February 1998 / Revised version: 11 June 1998 相似文献
17.
Global random attractors are uniquely determined by attracting deterministic compact sets 总被引:3,自引:0,他引:3
Hans Crauel 《Annali di Matematica Pura ed Applicata》1999,176(1):57-72
It is shown that for continuous dynamical systems an analogue of the Poincaré recurrence theorem holds for Ω-limit sets. A
similar result is proved for Ω-limit sets of random dynamical systems (RDS) on Polish spaces. This is used to derive that a random set which attracts every (deterministic) compact set has full measure
with respect to every invariant probability measure for theRDS. Then we show that a random attractor coincides with the Ω-limit set of a (nonrandom) compact set with probability arbitrarily
close to one, and even almost surely in case the base flow is ergodic. This is used to derive uniqueness of attractors, even
in case the base flow is not ergodic.
Entrata in Redazione il 10 marzo 1997. 相似文献
18.
Ibrahim A. Ahmad 《Annals of the Institute of Statistical Mathematics》1981,33(1):375-383
Summary The conditioned central limit theorem for the vector of maximum partial sums based on independent identically distributed
random vectors is investigated and the rate of convergence is discussed. The conditioning is that of Rényi (1958,Acta Math. Acad. Sci. Hungar.,9, 215–228). Analogous results for the vector of partial sums are obtained.
University of Petroleum and Minerals 相似文献
19.
On complete convergence for weighted sums of asymptotically linear negatively dependent random field
In this paper we establish the complete convergence for weighted sums of asymptotically linear negatively quadrant dependent random field, which contains a linear negatively quadrant dependent field and a ρ∗-mixing random field. 相似文献
20.
The object of the present investigation is to show that the elegant asymptotic almost-sure representation of a sample quantile for independent and identically distributed random variables, established by Bahadur [1] holds for a stationary sequence of φ-mixing random variables. Two different orders of the remainder term, under different φ-mixing conditions, are obtained and used for proving two functional central limit theorems for sample quantiles. It is also shown that the law of iterated logarithm holds for quantiles in stationary φ-mixing processes. 相似文献