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1.
In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence (centered at the sample mean) converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions.  相似文献   

2.
设{Xi}∞i=1是标准化强相依非平稳高斯序列,记Sn=∑Xi,σn=√var(Sn),Mktn为X1,X2,…,Xtn的第k个最大值,Ntn为X1,X2,…,Xtn对水平μn(x)的超过数形成的点过程,tn是-列单调增加的正整数列,在一定条件下得到Ntn与Sn/σn,Mktn与Sn/σn的联合渐近分布.  相似文献   

3.
设{X_i}_(i=1)~∞是标准化非平稳高斯序列,N_n为X_1,X_2,…,X_n依次对水平μ_(n1),μ_(n2),…,μ_(nn)的超过数形成的点过程.记Υ_(ij)=X_iX_j,S_n=■X_i.当Υ_(ij)满足一定条件时,证明了N_n依分布收敛到Poisson过程,且N_n与S_n渐近独立.  相似文献   

4.
强相依高斯序列超过数点过程与部分和的联合渐近分布   总被引:7,自引:3,他引:4  
(Xn)为标准化平稳高斯序列,pn=EX1Xn+1,Nn为X1,X2,…,Xn对水平un=x/an+bn的超过数形成的点过程,Mn^(k)为X1,X2,…,Xn的第k个最大值,Sn=(n)∑(i=1)Xi,pnlogn→r∈(0,∞)时,得到Nn与Sn、Mn^(k)与Sn的联合渐近分布。  相似文献   

5.
He and Xia (1997, Stochastic Processes Appl. 68, pp. 101–111) gave some error bounds for a Wasserstein distance between the distributions of the partial sum process of a Markov chain and a Poisson point process on the positive half-line. However, all these bounds increase logarithmically with the mean of the Poisson point process. In this paper, using the coupling method and a general deep result for estimating the errors of Poisson process approximation in Brown and Xia (2001, Ann. Probab. 29, pp. 1373–1403), we give a new error bound for the above Wasserstein distance. In contrast to the previous results of He and Xia (1997), our new error bound has no logarithm anymore and it is bounded and asymptotically remains constant as the mean increases.  相似文献   

6.
张玲 《应用数学学报》2006,29(1):111-115
{X_n,n≥1)是标准高斯序列,T_(ij)=cov(X_i,X_j)。本文在强相依条件rijlog(j-i)→r∈(0,∞)(j-i→ ∞)下,得到了高斯序列的最大值M_n与标准化部分和S_n=sum from i=1 to n(X_i/(E(sum from i=1 to n X_i)~2)/(1/2))  相似文献   

7.
We study the asymptotic relation among the maximum of continuous weakly and strongly dependent stationary Gaussian process, the maximum of this process sampled at discrete time points, and the partial sum of this process. It is shown that these two extreme values and the sum are asymptotically independent if the grid of the discrete time points is sufficiently sparse and the Gaussian process is weakly dependent, and asymptotically dependent if the grid points are Pickands grids or dense grids.  相似文献   

8.
In this paper we discuss connectedness of a design which is a Kronecker sum or a partial Kronecker row sum of any two equi-replicate and equi-block size designs.  相似文献   

9.
Let {X_n;,nge1} be a sequence of strictly stationary rho-mixing random variables with zero mean and finite variance. Using the weak convergence theorem and probability inequalities of rho-mixing sequence, under some proper conditions, we obtained general laws of precise asymptotics for partial sums of rho-mixing sequence.  相似文献   

10.
??Let {X_n;\,n\ge1} be a sequence of strictly stationary \rho-mixing random variables with zero mean and finite variance. Using the weak convergence theorem and probability inequalities of \rho-mixing sequence, under some proper conditions, we obtained general laws of precise asymptotics for partial sums of \rho-mixing sequence.  相似文献   

11.
For the variance of stationary renewal and alternating renewal processes Nn(·) the paper establishes upper and lower bounds of the form
?B1?varN8(0,x–Aλx?B2(0<x<∞)
, where λ=EN8(0,1), with constants A, B1 and B2 that depend on the first three moments of the interval distributions for the processes concerned. These results are consistent with the value of the constant A for a general stationary point process suggested by Cox in 1963 [1].  相似文献   

12.
Let {ξ j ; j ∈ ℤ+ d be a centered stationary Gaussian random field, where ℤ+ d is the d-dimensional lattice of all points in d-dimensional Euclidean space ℝd, having nonnegative integer coordinates. For each j = (j 1 , ..., jd) in ℤ+ d , we denote |j| = j 1 ... j d and for m, n ∈ ℤ+ d , define S(m, n] = Σ m<j≤n ζ j , σ2(|nm|) = ES 2 (m, n], S n = S(0, n] and S 0 = 0. Assume that σ(|n|) can be extended to a continuous function σ(t) of t > 0, which is nondecreasing and regularly varying with exponent α at b ≥ 0 for some 0 < α < 1. Under some additional conditions, we study limsup results for increments of partial sum processes and prove as well the law of the iterated logarithm for such partial sum processes. Research supported by NSERC Canada grants at Carleton University, Ottawa  相似文献   

13.
We show that in any aperiodic and ergodic dynamical system there exists a square integrable process the partial sums of which can be closely approximated by the partial sums of Gaussian i.i.d. random variables. For both weak and strong invariance principles hold.

  相似文献   


14.
Let {X(t), 0t1} be a Gaussian process with mean zero and stationary increments. Let 2(h) =EX 2(h) be nondecreasing and concave on (0,1). A sharp bound on the small ball probability ofX(·) is given in this paper.Research supported by Charles Phelps Taft Post-doctoral Fellowship of the University of Cincinnati and by the Fok Yingtung Education Foundation of China.  相似文献   

15.
Let {X(t), t ≥ 0} be a standard(zero-mean, unit-variance) stationary Gaussian process with correlation function r(·) and continuous sample paths. In this paper, we consider the maxima M(T) = max{X(t), t∈ [0, T ]} with random index TT, where TT /T converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of M(TT) exists under some additional conditions related to the correlation function r(·).  相似文献   

16.
Let {Xi, i?0} be a sequence of independent identically distributed random variables with finite absolute third moment. Then Darling and Erdös have shown that
for -∞<t<∞ where μn = max0?k?n k-12ki=0xi and Xn = (2 ln ln n)12. The result is extended to dependent sequences but assuming that {Xi} is a standard stationary Gaussian sequence with covariance function {ri}. When {Xi} is moderately dependent (e.g. when v(∑ni=1Xi) ? na, 0 < a < 2) we get
where Ha is a constant. In the strongly dependent case (e.g. when v(∑ni=1Xi) ? n2r(n)) we get
for-∞<t<∞.  相似文献   

17.
Let {Xn, n ? 1} be a sequence of identically distributed random variables, Zn = max {X1,…, Xn} and {un, n ? 1 } an increasing sequence of real numbers. Under certain additional requirements, necessary and sufficient conditions are given to have, with probability one, an infinite number of crossings of {Zn} with respect to {un}, in two cases: (1) The Xn's are independent, (2) {Xn} is stationary Gaussian and satisfies a mixing condition.  相似文献   

18.
设{X(t),0≤t≤T<+∞}是平稳高斯过程(可以是均方不可微的,即二阶谱矩可以是无限的),本文着重讨论当n→∞时,过程上穿过u的期望次数的渐近性质.  相似文献   

19.
In this paper we present an algorithm for finding a Nash equilibrium in a noncooperative normal formN-person game. More generally, the algorithm can be applied for solving a nonlinear stationary point problem on a simplotope, being the Cartesian product of several simplices. The algorithm solves the problem by solving a sequence of linear stationary point problems. Each problem in the sequence is solved in a finite number of iterations. Although the overall convergence cannot be proved, the method performs rather well. Computational results suggest that this algorithm performs at least as good as simplicial algorithms do.For the special case of a bi-matrix game (N=2), the algorithm has an appealing game-theoretic interpretation. In that case, the problem is linear and the algorithm always finds a solution. Furthermore, the equilibrium found in a bi-matrix game is perfect whenever the algorithm starts from a strategy vector at which all actions are played with positive probability.This research is part of the VF-program Co-operation and Competition, which has been approved by the Netherlands Ministery of Education and Sciences.  相似文献   

20.
We consider a Gaussian stationary sequence added by a pseudo-stationary trend and prove a limit theorem for joint distribution of its maximum and maximum of its subsequence. Supported by RFFI grants 07-01-00077 and 06-01-00454. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 1, pp. 58–67, January–March, 2007.  相似文献   

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