共查询到20条相似文献,搜索用时 15 毫秒
1.
Let Fn(x) be the empirical distribution function based on n independent random variables X1,…,Xn from a common distribution function F(x), and let be the sample mean. We derive the rate of convergence of to normality (for the regular as well as nonregular cases), a law of iterated logarithm, and an invariance principle for . 相似文献
2.
Given a polynomial , we calculate a subspace Gp of the linear space 〈X〉 generated by the indeterminates which is minimal with respect to the property (the algebra generated by Gp, and prove its uniqueness. Furthermore, we use this result to characterize the pairs (P,Q) of polynomials P(X1,…,Xn) and Q(X1,…,Xn) for which there exists an isomorphism T:〈X〉 →〈X〉 that “separates P from Q,” i.e., such that for some k(1<k<n) we can write P and Q as and respectively, where . 相似文献
3.
A compactificaton αX of a completely regular space X is “determined” by a subset F of C1(X) if αX is the smallest compactificaton of X to which each element of F extends, and is “generated” by F if the evaluation map , is an embedding and . Evidently, if F either determines or generates αX, then every elements of F has an extension to αX; whenever F satisfies this latter condition, the set of all such extensions is denoted Fα.A major results of our previous paper is that F determines αX if and only if Fα separates points of αX ? X. A major result of the present paper is that F generates αX if and only if Fα separates points of αX. 相似文献
4.
Sidney I. Resnick 《Stochastic Processes and their Applications》1973,1(1):67-82
{Xn,n?1} are i.i.d. random variables with continuous d.f. F(x). Xj is a record value of this sequence if Xj>max{X1,…,Xj?1}. Consider the sequence of such record values {XLn,n?1}. Set R(x)=-log(1?F(x)). There exist Bn > 0 such that . in probability (i.p.) iff i.p. iff → ∞ as x→∞ for all k>1. Similar criteria hold for the existence of constants An such that XLn?An → 0 i.p. Limiting record value distributions are of the form N(-log(-logG(x))) where G(·) is an extreme value distribution and N(·) is the standard normal distribution. Domain of attraction criteria for each of the three types of limit laws can be derived by appealing to a duality theorem relating the limiting record value distributions to the extreme value distributions. Repeated use is made of the following lemma: If , then XLn=Y0+…+Yn where the Yj's are i.i.d. and . 相似文献
5.
For fixed p (0 ≤ p ≤ 1), let {L0, R0} = {0, 1} and X1 be a uniform random variable over {L0, R0}. With probability p let {L1, R1} = {L0, X1} or = {X1, R0} according as ; with probability 1 ? p let {L1, R1} = {X1, R0} or = {L0, X1} according as , and let X2 be a uniform random variable over {L1, R1}. For n ≥ 2, with probability p let {Ln, Rn} = {Ln ? 1, Xn} or = {Xn, Rn ? 1} according as , with probability 1 ? p let {Ln, Rn} = {Xn, Rn ? 1} or = {Ln ? 1, Xn} according as , and let Xn + 1 be a uniform random variable over {Ln, Rn}. By this iterated procedure, a random sequence {Xn}n ≥ 1 is constructed, and it is easy to see that Xn converges to a random variable Yp (say) almost surely as n → ∞. Then what is the distribution of Yp? It is shown that the Beta, (2, 2) distribution is the distribution of Y1; that is, the probability density function of Y1 is g(y) = 6y(1 ? y) I0,1(y). It is also shown that the distribution of Y0 is not a known distribution but has some interesting properties (convexity and differentiability). 相似文献
6.
Roger Howe 《Journal of Functional Analysis》1979,32(3):297-303
Let (i, H, E) and (j, K, F) be abstract Wiener spaces and let α be a reasonable norm on E ? F. We are interested in the following problem: is () an abstract Wiener space ? The first thing we do is to prove that the setting of the problem is meaningfull: namely, i ? j is always a continuous one to one map from into . Then we exhibit an example which shows that the answer cannot be positive in full generality. Finally we prove that if F=Lp(X,,λ) for some σ-finite measure λ ? 0 then (X,,λ) is an abstract Wiener space. By-products are some new results on γ-radonifying operators, and new examples of Banach spaces and cross norms for which the answer is affirmative (in particular α = π the projective norm, and F=L1(X,,λ)). 相似文献
7.
Let (m?n) denote the linear space of all m × n complex or real matrices according as = or . Let c=(c1,…,cm)≠0 be such that c1???cm?0. The c-spectral norm of a matrix A?m×n is the quantity . where σ1(A)???σm(A) are the singular values of A. Let d=(d1,…,dm)≠0, where d1???dm?0. We consider the linear isometries between the normed spaces and , and prove that they are dual transformations of the linear operators which map (d) onto (c), where . 相似文献
8.
Let C(S) be the space of real-valued continuous functions on a compact metric space S. Let {Xn, n ? 1} be a sequence of independent identically distributed C(S)-valued random variables with mean zero and supt?sE[X12(t)] = 1. We show that the measures induced by ( converge weakly to a Gaussian measure on C(S) under different conditions on X1, one of which consolidates and extends results of Strassen and Dudley, Giné, and Dudley. Our method of proof is different from the methods employed by these authors. 相似文献
9.
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
10.
Let Mm,n(F) denote the space of all mXn matrices over the algebraically closed field F. A subspace of Mm,n(F), all of whose nonzero elements have rank k, is said to be essentially decomposable if there exist nonsingular mXn matrices U and V respectively such that for any element A, UAV has the form where A1 is iX(k–i) for some i?k. Theorem: If is a space of rank k matrices, then either is essentially decomposable or dim ?k+1. An example shows that the above bound on non-essentially-decomposable spaces of rank k matrices is sharp whenever n?2k–1. 相似文献
11.
Charles M Newman 《Journal of Functional Analysis》1973,14(1):44-61
It is shown that if φ(f) ∝Rdφ(y) f(y) dy is a Markoff random field and Xα are multiplicative functionals of φ (with E(Xα) = 1) which converge locally in L1, then there exists a locally Markoff random field such that . We choose φ to be the two-dimensional generalization of the Ornstein-Uhlenbeck velocity process and take Xα proportional to exp(?λ∝R2 : P(φ(y)) : gα(y) dy), where: P(φ(y)) : is a regularized even degree polynomial in φ(y). It is then proved that for an appropriate choice of gα → 1 and small λ, {Xα} does converge locally in L1 and that the corresponding is stationary. 相似文献
12.
Alain A. Lewis 《Mathematical Social Sciences》1985,9(3):197-247
Let 1M be a denumerately comprehensive enlargement of a set-theoretic structure sufficient to model R. If F is an internal 1finite subset of 1N such that , we define a class of 1finite cooperative games having the form , where A(F) is the internal algebra of the internal subsets of F, and is a set-function with , , and . If is the space of S-imputations of a game ΓF(1ν) such that , for some , then we prove that contains two nonempty subsets: and , termed the quasi-kernel and S-bargaining set, respectively. Both and are external solution concepts for games of the form ΓF (1ν) and are defined in terms of predicates that are approximate in infinitesimal terms. Furthermore, if L(Θ) is the Loeb space generated by the 1finitely additive measure space 〈F, A(F), UF〉, and if a game ΓF(1ν) has a nonatomic representation on L(Θ) with respect to S-bounded transformations, then the standard part of any element in is Loeb-measurable and belongs to the quasi-kernel of defined in standard terms. 相似文献
13.
Richard L. Tweedie 《Stochastic Processes and their Applications》1975,3(4):385-403
Let {Xn} be a ?-irreducible Markov chain on an arbitrary space. Sufficient conditions are given under which the chain is ergodic or recurrent. These extend known results for chains on a countable state space. In particular, it is shown that if the space is a normed topological space, then under some continuity conditions on the transition probabilities of {Xn} the conditions for ergodicity will be met if there is a compact set K and an ? > 0 such that whenever x lies outside K and is bounded, x ∈ K; whilst the conditions for recurrence will be met if there exists a compact K with for all x outside K. An application to queueing theory is given. 相似文献
14.
Alain A. Lewis 《Mathematical Social Sciences》1985,9(2):189-194
Let be an ω1-saturated enlargement in the sense of Keisler (1977) and let be a hyperfinite finite set in 1. Following the suggestion of Wesley (1971) we define a class of hyperfinite games of the form: , and show that measure-theoretic analogues of the kernel and bargaining set exist in this nonstandard setting such that their standard parts Loeb-measurable measurable on the Loeb space generated by the internal 1finitely additive measure . 相似文献
15.
Thomas G. Kurtz 《Stochastic Processes and their Applications》1978,6(3):223-240
A variety of continuous parameter Markov chains arising in applied probability (e.g. epidemic and chemical reaction models) can be obtained as solutions of equations of the form where , the Y1 are independent Poisson processes, and N is a parameter with a natural interpretation (e.g. total population size or volume of a reacting solution).The corresponding deterministic model, satisfies Under very general conditions limN→∞XN(t)=X(t) a.s. The process XN(t) is compared to the diffusion processes given by and Under conditions satisfied by most of the applied probability models, it is shown that XN,ZN and V can be constructed on the same sample space in such a way that and 相似文献
16.
Let denote the set of n×nD-stable matrices with entries from . A characterization of the interior of considered as subset of the topological space n2, is given for the cases . 相似文献
17.
N.J Kalton 《Journal of Functional Analysis》1981,42(3):299-337
We prove a number of results concerning isomorphisms between spaces of the type Lp(X), where X is a separable p-Banach space and 0 < p < 1. Our results imply that the quotient of Lp([0, 1] × [0, 1]) by the subspace of functions depending only on the first variable is not isomorphic to Lp, answering a question of N. T. Peck. More generally if 0 is a sub-σ-algebra of the Borel sets of [0, 1], then , 0) is isomorphic to Lp if and only if Lp([0, 1], B0) is complemented. We also show that Lp has, up to isomorphism, at most one complemented subspace non-isomorphic to Lp and classify completely those spaces X for which . In particular if then or is finite-dimensional. If X has trivial dual and . 相似文献
18.
Rym Worms 《Comptes Rendus Mathematique》2002,334(8):709-712
We compare assumptions used in [4] in order to study the rate of convergence to 0, as u→s+(F), of , where is the survival function of the excesses over u, s+(F)=sup{x,F(x)<1} is the upper end point of the distribution function (d.f.) F and is the survival function of the Generalized Pareto Distribution, with assumptions used in [2] in order to study the rate of convergence to 0, as n→+∞, of , where Hγ is the d.f. of an extreme value distribution. In each case, an indicator linked to regular variation assumptions had been introduced. We characterize situations where these two indicators coincide, and others where they are different. To cite this article: R. Worms, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 709–712. 相似文献
19.
Let , let , where g2 and g3 are coefficients of the elliptic curve: Y2 = 4X3 ? g2X ? g3 over a finite field and Δ = g23 ? 27g32 and let . Then the p-adic cohomology theory will be applied to compute explicitly the zeta matrices of the elliptic curves, induced by the pth power map on the free -module . Main results are; Theorem 1.1: X2dY and YdX are basis elements for ; Theorem 1.2: YdX, X2dY, Y?1dX, Y?2dX and XY?2dX are basis elements for , where is a lifting of X, and all the necessary recursive formulas for this explicit computation are given. 相似文献
20.
《Topology and its Applications》2004,135(1-3):231-247
A topological system (X,f) is -transitive if for each pair of opene subsets U and V of X, , where is a collection of subsets of which is hereditary upward. (X,f) is -mixing if (X×X,f×f) is -transitive. In this paper -mixing systems are characterized in terms of the chaoticity of the systems. Moreover, weak disjointness is studied via family. We will give conditions such that a dual theorem of the Weiss–Akin–Glasner theorem holds. Examples with this dual theorem fails for some “good” families are obtained. 相似文献