共查询到20条相似文献,搜索用时 343 毫秒
1.
Given \s{ Xi, i 1\s} as non-stationary strong mixing (n.s.s.m.) sequence of random variables (r.v.'s) let, for 1 i n and some γ ε [0, 1], F1(x)=γP(Xi<x)+(1-γ)P(Xix) and Ii(x)=γI(Xi<x)+(1-γ)I(Xix) . For any real sequence \s{ Ci\s} satisfying certain conditions, let . In this paper an exponential type of bound for P(Dn ), for any >0, and a rate for the almost sure convergence of Dn are obtained under strong mixing. These results generalize those of Singh (1975) for the independent and non-identically distributed sequence of r.v.'s to the case of strong mixing. 相似文献
2.
For a 1-dependent stationary sequence { Xn} we first show that if u satisfies p1= p1( u)= P( X1> u)0.025 and n>3 is such that 88 np131, then P{max(X1,…,Xn)u}=ν·μn+O{p13(88n(1+124np13)+561)}, n>3, where ν=1−p2+2p3−3p4+p12+6p22−6p1p2,μ=(1+p1−p2+p3−p4+2p12+3p22−5p1p2)−1 with pk=pk(u)=P{min(X1,…,Xk)>u}, k1 and From this result we deduce, for a stationary T-dependent process with a.s. continuous path { Ys}, a similar, in terms of P{max 0skTYs< u}, k=1,2 formula for P{max 0stYsu}, t>3 T and apply this formula to the process Ys= W( s+1)− W( s), s0, where { W( s)} is the Wiener process. We then obtain numerical estimations of the above probabilities. 相似文献
3.
This paper presents the finding that the invocation of new words in human language samples is governed by a slowly changing Poisson process. The time dependent rate constant for this process has the form λ(t) = λ1(1−λ2t)e-λ2t+λ3(1−λ4t)e-λ4t+λ5 , where . This form implies that there are opening, middle and final phases to the introduction of new words, each distinguished by a dominant rate constant, or equivalently, rate of decay. With the occasional exception of the phase transition from beginning to middle, the rate λ(t) decays monotonically. Thus, λ(t) quantifies how the penchant of humans to introduce new words declines with the progression of their narratives, written or spoken. 相似文献
4.
Oscillation criteria for the second-order half-linear differential equation [r(t)|ξ′(t)|−1 ξ′(t)]′ + p(t)|ξ(t)|−1ξ(t)=0, t t0 are established, where > 0 is a constant and
exists for t [ t0, ∞). We apply these results to the following equation: where
, D = ( D1,…, DN), Ω a = x
N : |x| ≥ a} is an exterior domain, and c C([a, ∞),
), n > 1 and N ≥ 2 are integers. Here, a > 0 is a given constant. 相似文献
5.
In 1994, van Trung (Discrete Math. 128 (1994) 337–348) [9] proved that if, for some positive integers d and h, there exists an Sλ( t, k, v) such that then there exists an Sλ(v−t+1)( t, k, v+1) having v+1 pairwise disjoint subdesigns Sλ( t, k, v). Moreover, if Bi and Bj are any two blocks belonging to two distinct such subdesigns, then d| Bi∩ Bj|< k− h. In 1999, Baudelet and Sebille (J. Combin. Des. 7 (1999) 107–112) proved that if, for some positive integers, there exists an Sλ( t, k, v) such that where m=min{ s, v− k} and n=min{ i, t}, then there exists an having
pairwise disjoint subdesigns Sλ( t, k, v). The purpose of this paper is to generalize these two constructions in order to produce a new recursive construction of t-designs and a new extension theorem of t-designs. 相似文献
6.
In the present paper, we consider the following generalization of Besicovitch functions. Let {λ n} satisfy Hadamard condition, write We are interested in the intrinsic relationship among the coefficients {an}, the modulus of continuity of f and the upper Box dimension of graph of f. Especially, constructive structure of the function f which can be deduced from the (upper) Box dimension is a very interesting subject, and is hardly ever touched upon as far as we are aware. 相似文献
7.
Using the integral average method, we establish some oscillation criteria of Kamenev type and Yan type for the nonlinear system of differential equation where the functions bi( t) ( i = 1, 2) are nonnegative and summable on each finite segment of the interval Z0, ∞), λ i > 0 ( i = 1,2) with λ 1 λ 2 = 1. 相似文献
8.
This paper considers a class of nonlinear difference equations Δ3yn + ƒ(n, yn, yn−r) = 0, n N (n0) . A necessary and sufficient condition for the existence of a bounded nonoscillatory solution is given. 相似文献
9.
Consider the first-order neutral nonlinear difference equation of the form , where τ > 0, σ i ≥ 0 ( i = 1, 2,…, m) are integers, { pn} and { qn} are nonnegative sequences. We obtain new criteria for the oscillation of the above equation without the restrictions Σ n=0∞ qn = ∞ or Σ n=0∞ nqn Σ j=n∞ qj = ∞ commonly used in the literature. 相似文献
10.
A weighted graph ( G, w) is a graph G together with a positive weight-function on its vertex set w : V( G)→R >0. The weighted domination number γ w( G) of ( G, w) is the minimum weight w( D)=∑ vDw( v) of a set DV( G) such that every vertex xV( D)− D has a neighbor in D. If ∑ vV(G)w( v)=| V( G)|, then we speak of a normed weighted graph. Recently, we proved that for normed weighted bipartite graphs ( G, w) of order n such that neither G nor the complement
has isolated vertices. In this paper we will extend these Nordhaus–Gaddum-type results to triangle-free graphs. 相似文献
11.
We shall establish some new criteria for the oscillation of all solutions of higher-order difference equations of the form δm(xn-xn-r)+qnf(xn-g=0, m1 相似文献
12.
Let X1, X2, … be independent identically distributed random variables. Then, Hsu and Robbins (1947) together with Erdös (1949, 1950) have proved that , if and only if E[X21] < ∞ and E[X1] = 0. We prove that there are absolute constants C1, C2 (0, ∞) such that if X1, X2, … are independent identically distributed mean zero random variables, then c1λ−2 E[X12·1{|X1|λ}]S(λ)C2λ−2 E[X12·1{|X1|λ}] , for every λ > 0. 相似文献
13.
This paper examine all sums of the form where W is a classical Weyl group, X is a one-dimensional character of W, and d(π) is the descent statistic. This completes a picture which is known when W is the symmetric group Sn (the Weyl group An−1). Surprisingly, the answers turn out to be simpler and generalize further for the other classical Weyl groups Bn( Cn) and Dn. The B n, case uses sign-reversing involutions, while the Dn case follows from a result of independent interest relating statistics for all three groups. 相似文献
14.
This paper gives a parallel computing scheme for minimizing a twice continuously differentiable function with the form where x = ( xT1,…, xTm) T and xi Rni, ∑ mi = 1ni = n, and n a very big number. It is proved that we may use m parallel processors and an iterative procedure to find a minimizer of ƒ( x). The convergence and convergence rate are given under some conditions. The conditions for finding a global minimizer of ƒ( x by using this scheme are given, too. A similar scheme can also be used parallelly to solve a large scale system of nonlinear equations in the similar way. A more general case is also investigated. 相似文献
15.
We prove that for λ ≥ 0, p ≥ 3, there exists an open ball B L2(0,1) such that the problem − (|u′|p−2 u′)′ − λ|u|p−2u = f, in (0,1) , subject to certain separated boundary conditions on (0,1), has a solution for f B. 相似文献
16.
Let {ζ k} be the normalized sums corresponding to a sequence of i.i.d. variables with zero mean and unit variance. Define random measures and let G be the normal distribution. We show that for each continuous function h satisfying ∫ hd G<∞ and a mild regularity assumption, one has a.s. 相似文献
17.
We establish an explicit formula for the number of Latin squares of order n: , where Bn is the set of n× n(0,1) matrices, σ 0( A is the number of zero elements of the matrix A and per A is the permanent of the matrix A. 相似文献
18.
In this paper, we provide a solution of the quadrature sum problem of R. Askey for a class of Freud weights. Let r> 0, b (− ∞, 2]. We establish a full quadrature sum estimate 1 p < ∞, for every polynomial P of degree at most n + rn1/3, where W2 is a Freud weight such as exp(−¦ x¦ ), > 1, λ jn are the Christoffel numbers, xjn are the zeros of the orthonormal polynomials for the weight W2, and C is independent of n and P. We also prove a generalisation, and that such an estimate is not possible for polynomials P of degree M = m( n) if m( n) = n + ξ nn1/3, where ξ n → ∞ as n → ∞. Previous estimates could sum only over those xjn with ¦ xjn¦ σ x1n, some fixed 0 < σ < 1. 相似文献
19.
For the pth-order linear ARCH model, , where 0 > 0, i 0, I = 1, 2, …, p, { t} is an i.i.d. normal white noise with Et = 0, Et2 = 1, and t is independent of { Xs, s < t}, Engle (1982) obtained the necessary and sufficient condition for the second-order stationarity, that is, 1 + 2 + ··· + p < 1. In this note, we assume that t has the probability density function p( t) which is positive and lower-semicontinuous over the real line, but not necessarily Gaussian, then the geometric ergodicity of the ARCH( p) process is proved under Et2 = 1. When t has only the first-order absolute moment, a sufficient condition for the geometric ergodicity is also given. 相似文献
20.
Consider two transient Markov processes ( Xvt) tεR·, ( Xμt) tεR· with the same transition semigroup and initial distributions v and μ. The probability spaces supporting the processes each are also assumed to support an exponentially distributed random variable independent of the process. We show that there exist (randomized) stopping times S for (Xvt), T for (Xμt) with common final distribution, L(XvS|S < ∞) = L(XμT|T < ∞), and the property that for t < S, resp. t < T, the processes move in disjoint portions of the state space. For such a coupling (S, T) it is shown where
denotes the bounded harmonic functions of the Markov transition semigroup. Extensions, consequences and applications of this result are discussed. 相似文献
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