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1.
郭晓燕  孔繁超 《数学季刊》2007,22(2):282-289
This paper is a further investigation of large deviations for sums of random variables S_n=sum form i=1 to n X_i and S(t)=sum form i=1 to N(t) X_i,(t≥0), where {X_n,n≥1) are independent identically distribution and non-negative random variables, and {N(t),t≥0} is a counting process of non-negative integer-valued random variables, independent of {X_n,n≥1}. In this paper, under the suppose F∈G, which is a bigger heavy-tailed class than C, proved large deviation results for sums of random variables.  相似文献   

2.
In this paper the large deviation results for partial and random sums Sn-ESn=n∑i=1Xi-n∑i=1EXi,n≥1;S(t)-ES(t)=N(t)∑i=1Xi-E(N(t)∑i=1Xi),t≥0are proved, where {N(t); t≥ 0} is a counting process of non-negative integer-valued random variables, and {Xn; n ≥ 1} are a sequence of independent non-negative random variables independent of {N(t); t ≥ 0}. These results extend and improve some known conclusions.  相似文献   

3.
We prove large deviation results on the partial and random sums Sn = ∑i=1n Xi,n≥1; S(t) = ∑i=1N(t) Xi, t≥0, where {N(t);t≥0} are non-negative integer-valued random variables and {Xn;n≥1} are independent non-negative random variables with distribution, Fn, of Xn, independent of {N(t); t≥0}. Special attention is paid to the distribution of dominated variation.  相似文献   

4.
ON ESTIMATING THE HIDDEN PERIODICITIES IN LINEAR TIME SERIES MODELS   总被引:3,自引:0,他引:3  
In this paper the tollowing modelX(n)=sum from j=1 to p α_je~(inλj)+ξ_nis considered,where p,λ_1,λ_2,…,λ_p,are constants α=(α_1,α_2,…,α_p) is a random vector and {ξ_n;n=0,±1,±2,…} is a wide-sense stationary sequence with zero means.In [4],theorem about thestrong consistent estimates of λ_1,λ_2.…,λ_p and α are proved under the assumption that α is a constantvector and p and δ are known constants such that0<δ<(?){λ_i-λ_j}.The main purpose of the present paper is to prove theorems on the strong consistent estimates ofparameters p,λ_1,λ_2,…,λ_p and random vector α without knowing p and δ.Numerical examples arealso given to illustrate our method of estimation.  相似文献   

5.
The ( f,d_n) -summability method is defined as follows^[1,4]: Let f be a nonconstant function, analytic in |z | < R for R > l, and let {d_n} be a sequence of complex numbers,such that for all n,$d_n \ne -f(1)$.Suppose that the elements of the metrix A = (a_nk) are given by the relations $a_00=1,a_0k=0(k \geq 1)$ $[\prod\limits_{j = 1}^n {\frac{{f(z) + {d_j}}}{{f(1) + {d_j}}} = \sum\limits_{k = 0}^\infty {{a_{nk}}{z^k}} } \]$ A sequence {S_n} is said to be ( f, d_n), —summable to s, if \sigma_n = \sum\limits_{k=0}^\infty \arrow s as n \arrow \infty. The ( f, d_n) —summability method is said to be non-negative if for all n, d_n> 0 and the Maclaurin coefficients of f are real and non-negative. The Lebesgue constants for the ( f,d_n)-method are defined by $L_n(A)=2/\pi \int_0^\pi /2 {\frac{|\sum\limits_{k=0}^\infty {a_nk sin(2k+1)t|}{sint}dt}$ In this parer we prove the following two theorems.  相似文献   

6.
Let {a_n} and {b_n}be any two sequences of non-negative numbers such that 01).Then Hardy-Riesz′s extension of the Hilbert inequality can be sharpened to the form  相似文献   

7.
Consider the partly linear regression model ,where yi's are responses, xi = (xi1, xi2,…,xip)' and ti ∈T are known and nonrandom design points, T is a compact set in the real line is an unknown parameter vector, g(·) is an unknown function and {Ei} isa linear process, i.e., random variables with zeromean and variance o2e. Drawing upon B-spline estimation of g(·) and least squares estimation of 0, we construct estimators of the autocovariances of {Ei}- The uniform strong convergence rate of these estimators to their true values is then established. These results not only are a compensation for those of [23], but also have some application in modeling error structure. When the errors {Ei} are an ARMA process, our result can be used to develop a consistent procedure for determining the order of the ARMA process and identifying the non-zero coefficients of the process. Moreover, our result can be used to construct the asymptotically efficient estimators for parameters in the ARMA error process.  相似文献   

8.
In this paper, we study the problem of a variety of p, onlinear time series model Xn+ 1= TZn+1(X(n), … ,X(n - Zn+l), en+1(Zn+1)) in which {Zn} is a Markov chain with finite state space, and for every state i of the Markov chain, {en(i)} is a sequence of independent and identically distributed random variables. Also, the limit behavior of the sequence {Xn} defined by the above model is investigated. Some new novel results on the underlying models are presented.  相似文献   

9.
A property(C) for permutation pairs is introduced. It is shown that if a pair{π_1, π_2} of permutations of(1,2,…,n) has property(C),then the D-type map Φ_(π_1,π_2) on n× n complex matrices constructed from {π_1,π_2} is positive. A necessary and sufficient condition is obtained for a pair {π_1,π_2} to have property(C),and an easily checked necessary and sufficient condition for the pairs of the form {π~p,π~q} to have property(C) is given, whereπ is the permutation defined by π(i) = i + 1 mod n and 1≤ p q≤ n.  相似文献   

10.
We prove the following result in this paper: Let(X, ζ, △) be a T—complete Menger space. If {T_i, i=1, 2, …} are a sequence of the self mapping of the contractive type on X and {m_i(x), i=1, 2, …} are the functional sequence satisfying m_i(x)|m(T_i(x)), i=1, 2, …, then {T_i, i=1, 2, …} have a common fixed point.This result is a generalization to the result obtained in I. Istratescu [7, 14]. Other results are proved concerning the fixed point theorems for G valued metric space. The concept, the embedded theorem of S. M. space, is discussed and its relation to the existence of fixed point for above mapping is also discussed in S. M. space.  相似文献   

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