共查询到20条相似文献,搜索用时 32 毫秒
1.
Ko-Wei Lih 《Journal of Combinatorial Theory, Series A》1980,29(2):182-185
Let |X| = n > 0, |Y| = k > 0, and Y ? X. A family A of subsets of X is a Sperner family of X over Y if A1A2 for every pair of distinct members of A and every member of A has a nonempty intersection with Y. The maximum cardinality f(n, k) of such a family is determined in this paper. . 相似文献
2.
Simeon M. Berman 《Journal of multivariate analysis》1978,8(1):30-44
Let R(s, t) be a continuous, nonnegative, real valued function on a ≤ s ≤ t ≤ b. Suppose , , and in the interior of the domain. Then the extension of R to a symmetric function on [a, b] × [a, b] is a covariance function. Such a covariance is called biconvex. Let X(t) be a Gaussian process with mean 0 and biconvex covariance. X has a representation as a sum of simple moving averages of white noises on the line and plane. The germ field of X at every point t is generated by X(t) alone. X is locally nondeterministic. Under an additional assumption involving the partial derivatives of R near the diagonal, the local time of the sample function exists and is jointly continuous almost surely, so that the sample function is nowhere differentiable. 相似文献
3.
M.E Bock 《Journal of multivariate analysis》1985,17(2):127-147
Let X be a p-dimensional random vector with density f(6X?θ6) where θ is an unknown location vector. For p ≥ 3, conditions on f are given for which there exist minimax estimators θ?(X) satisfying 6Xt6 · 6θ?(X) ? X6 ≤ C, where C is a known constant depending on f. (The positive part estimator is among them.) The loss function is a nondecreasing concave function of 6θ?? θ62. If θ is assumed likely to lie in a ball in p, then minimax estimators are given which shrink from the observation X outside the ball in the direction of P(X) the closest point on the surface of the ball. The amount of shrinkage depends on the distance of X from the ball. 相似文献
4.
Loren D. Pitt 《Journal of multivariate analysis》1978,8(1):45-54
For Gaussian vector fields {X(t) ∈ Rn:t ∈ Rd} we describe the covariance functions of all scaling limits Y(t) = limα↓0 B?1(α) X(αt) which can occur when B(α) is a d × d matrix function with B(α) → 0. These matrix covariance functions are found to be homogeneous in the sense that for some matrix L and each α > 0, . Processes with stationary increments satisfying (1) are further analysed and are found to be natural generalizations of Lévy's multiparameter Brownian motion. 相似文献
5.
H.J Ryser 《Journal of Combinatorial Theory, Series A》1982,32(2):162-177
6.
Let Ω be a finite set with k elements and for each integer let (n-tuple) and and aj ≠ aj+1 for some 1 ≦ j ≦ n ? 1}. Let {Ym} be a sequence of independent and identically distributed random variables such that P(Y1 = a) = k?1 for all a in Ω. In this paper, we obtain some very surprising and interesting results about the first occurrence of elements in and in Ω?n with respect to the stochastic process {Ym}. The results here provide us with a better and deeper understanding of the fair coin-tossing (k-sided) process. 相似文献
7.
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
8.
Let Ω = {1, 0} and for each integer n ≥ 1 let (n-tuple) and for all k = 0,1,…,n. Let {Ym}m≥1 be a sequence of i.i.d. random variables such that . For each A in , let TA be the first occurrence time of A with respect to the stochastic process {Ym}m≥1. R. Chen and A.Zame (1979, J. Multivariate Anal. 9, 150–157) prove that if n ≥ 3, then for each element A in , there is an element B in such that the probability that TB is less than TA is greater than . This result is sharpened as follows: (I) for n ≥ 4 and 1 ≤ k ≤ n ? 1, each element A in , there is an element B also in such that the probability that TB is less than TA is greater than ; (II) for n ≥ 4 and 1 ≤ k ≤ n ? 1, each element A = (a1, a2,…,an) in , there is an element C also in such that the probability that TA is less than TC is greater than if n ≠ 2m or n = 2m but ai = ai + 1 for some 1 ≤ i ≤ n?1. These new results provide us with a better and deeper understanding of the fair coin tossing process. 相似文献
9.
Two square matrices A and B over a ring R are semisimilar, written AB, if YAX=B and XBY=A for some (possibly rectangular) matrices X, Y over R. We show that if A and B have the same dimension, and if the ring is a division ring , then AB if and only if A2 is similar to B2 and rank(Ak)=rank(Bk), k=1,2,… 相似文献
10.
Luc Devroye 《Journal of multivariate analysis》1982,12(1):72-79
If X1,…,Xn are independent identically distributed Rd-valued random vectors with probability measure μ and empirical probability measure μn, and if is a subset of the Borel sets on Rd, then we show that P{supA∈|μn(A)?μ(A)|≥ε} ≤ cs(, n2)e?2n∈2, where c is an explicitly given constant, and s(, n) is the maximum over all (x1,…,xn) ∈ Rdn of the number of different sets in {{x1…,xn}∩A|A ∈}. The bound strengthens a result due to Vapnik and Chervonenkis. 相似文献
11.
P.S Milojević 《Journal of Mathematical Analysis and Applications》1978,65(2):468-502
Let X and Y be real normed spaces with an admissible scheme Γ = {En, Vn; Fn, Wn} and T: X → 2YA-proper with respect to Γ such that dist(y, A(x)) < kc(∥ x ∥) for all y in T(x) with ∥ x ∥ ? R for some R > 0 and k > 0, where c: R+ → R+ is a given function and A: X → 2Y a suitable possibly not A-proper mapping. Under the assumption that either T or A is odd or that (u, Kx) ? 0 for all u in T(x) with , we obtain (in a constructive way) various generalizations of the first Fredholm theorem. The unique approximation-solvability results for the equation T(x) = f with T such that T(x) ? T(y) ?A(x ? y) for x, y in X or T is Fréchet differentiable are also established. The abstract results for A-proper mappings are then applied to the (constructive) solvability of some boundary value problems for quasilinear elliptic equations. Some of our results include the results of Lasota, Lasota-Opial, Hess, Ne?as, Petryshyn, and Babu?ka. 相似文献
12.
Let T be a rooted tree structure with n nodes a1,…,an. A function f: {a1,…,an} into {1 < ? < k} is called monotone if whenever ai is a son of aj, then f(ai) ≥ f(aj). The average number of monotone bijections is determined for several classes of tree structures. If k is fixed, for the average number of monotone functions asymptotic equivalents of the form c · ??nn? (n → ∞) are obtained for several classes of tree structures. 相似文献
13.
The following results are proved: Let A = (aij) be an n × n complex matrix, n ? 2, and let k be a fixed integer, 1 ? k ? n ? 1.(1) If there exists a monotonic G-function f = (f1,…,fn) such that for every subset of S of {1,…,n} consisting of k + 1 elements we have then the rank of A is ? n ? k + 1. (2) If A is irreducible and if there exists a G-function f = (f1,…,fn) such that for every subset of S of {1,…,n} consisting of k + 1 elements we have then the rank of A is ? n ? k + 1 if k ? 2, n ? 3; it is ? n ? 1 if k = 1. 相似文献
14.
Let = (1, 2, …, n)′ be the least-squares estimator of θ = (θ1, θ2, …, θn)′ by the realization of the process y(t) = Σk = 1nθkfk(t) + ξ(t) on the interval T = [a, b] with f = (f1, f2, …, fn)′ belonging to a certain set X. The process satisfies E(ξ(t))≡0 and has known continuous covariance r(s, t) = E(ξ(s)ξ(t)) on T × T. In this paper, A-, D-, and Ds-optimality are used as criteria for choosing f in X. A-, D-, and Ds-optimal models can be constructed explicitly by means of r. 相似文献
15.
Christer Borell 《Journal of Mathematical Analysis and Applications》1973,41(2):300-312
We study certain functionals and obtain an inverse Hölder inequality for n functions f1a1,…,fnan (fk concave, 1 dimension).We also prove a multidimensional inverse Hölder inequality for n functions f1,…,fn, where .Finally we give an inverse Minkowski inequality for concave functions. 相似文献
16.
Let be a real or complex n × n interval matrix. Then it is shown that the Neumann series is convergent iff the sequence {k} converges to the null matrix , i.e., iff the spectral radius of the real comparison matrix constructed in [2] is less than one. 相似文献
17.
Let (Ω, , μ) be a measure space, a separable Banach space, and 1 the space of all bounded conjugate linear functionals on . Let f be a weak1 summable positive B(1)-valued function defined on Ω. The existence of a separable Hilbert space , a weakly measurable B()-valued function Q satisfying the relation is proved. This result is used to define the Hilbert space L2,f of square integrable operator-valued functions with respect to f. It is shown that for B+(1)-valued measures, the concepts of weak1, weak, and strong countable additivity are all the same. Connections with stochastic processes are explained. 相似文献
18.
A function f(x) defined on = 1 × 2 × … × n where each i is totally ordered satisfying f(x ∨ y) f(x ∧ y) ≥ f(x) f(y), where the lattice operations ∨ and ∧ refer to the usual ordering on , is said to be multivariate totally positive of order 2 (MTP2). A random vector Z = (Z1, Z2,…, Zn) of n-real components is MTP2 if its density is MTP2. Classes of examples include independent random variables, absolute value multinormal whose covariance matrix Σ satisfies ?DΣ?1D with nonnegative off-diagonal elements for some diagonal matrix D, characteristic roots of random Wishart matrices, multivariate logistic, gamma and F distributions, and others. Composition and marginal operations preserve the MTP2 properties. The MTP2 property facilitate the characterization of bounds for confidence sets, the calculation of coverage probabilities, securing estimates of multivariate ranking, in establishing a hierarchy of correlation inequalities, and in studying monotone Markov processes. Extensions on the theory of MTP2 kernels are presented and amplified by a wide variety of applications. 相似文献
19.
Let Xt be a homogeneous Markov process generated by the weak infinitesimal operator A. Let be the class of functions f such that f, f2?DA, the domain of A. The main result of this paper states that for ? ∈ can be represented by a stochastic integral and other terms. If the process is generated by a second order differential operator (with ‘poor’ coefficients possibly) on C02(Rd) then the process itself can be represented as the solution of an Itô stochastic differential equation. 相似文献