Author Keywords: Bounded in probability; convergence in probability; cotype; uniform tightness condition 相似文献
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1.
A.K. Katsaras 《Journal of Mathematical Analysis and Applications》2010,365(1):342-357
For a separating algebra R of subsets of a set X, E a complete Hausdorff non-Archimedean locally convex space and m:R→E a bounded finitely additive measure, we study some of the properties of the integrals with respect to m of scalar-valued functions on X. The concepts of convergence in measure, with respect to m, and of m-measurable functions are introduced and several results concerning these notions are given. 相似文献
2.
Let X be a (real) separable Banach space, let {Vk} be a sequence of random elements in X, and let {ank} be a double array of real numbers such that limn→∞ ank = 0 for all k and Σ∞k=1 |ank| ≤ 1 for all n. Define Sn = Σnk=1 ank(Vk − EVk). The convergence of {Sn} to zero in probability is proved under conditions on the coordinates of a Schauder basis or on the dual space of X and conditions on the distributions of {Vk}. Convergence with probability one for {Sn} is proved for separable normed linear spaces which satisfy Beck's convexity condition with additional restrictions on {ank} but without distribution conditions for the random elements {Vk}. Finally, examples of arrays {ank}, spaces, and applications of these results are considered. 相似文献
3.
Xiang Chen Wang 《Statistics & probability letters》1990,10(5):391-396
Let B be a separable Banach space. The following is one of the results proved in this paper. The Banach space B is of cotype p if and only if
1. dn, n 1, has no subsequence converging in probability, and
2. ∑n 1|an|p < ∞ whenever ∑n 1andn converges almost surely are equivalent for every sequence dn, n 1, of symmetric independent random elements taking values in B.
4.
Stephen James Wolfe 《Journal of multivariate analysis》1983,13(4):534-538
It is shown that every full eA decomposable probability measure on Rk, where A is a linear operator all of whose eigenvalues have negative real part, is either absolutely continuous with respect to Lebesgue measure or continuous singular with respect to Lebesgue measure. This result is used to characterize the continuity properties of random variables that are limits of solutions of certain stochastic difference equations. 相似文献
5.
We characterize uniform convergence rates in Sobolev and local Sobolev spaces for multiresolution analyses. 相似文献
6.
Robert M Burton 《Statistics & probability letters》1985,3(6):315-316
If a sequence of random variables Xn converges to X in probability we know little about the pointwise behavior Xn(ω). In this note we show that if Xn converges to X quickly enough (for example, like n?α for α > 0) then, for almost all ω, Xn(ω) converges to X(ω) outside a set of density zero. 相似文献
7.
The main aim of this paper is to prove that the logarithmic means of quadratical partial sums of the double Walsh-Fourier series does not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of LlnL(I2), the set of the functions having logarithmic means of quadratical partial sums of the double Walsh-Fourier series convergent in measure is of first Baire category. 相似文献
8.
The purpose of this paper is to present some results on linear programming in measure spaces (LPM). We prove that, under certain conditions, the optimal value of an LPM is equal to the optimal value of the dual problem (DLPM). We also present two algorithms for solving various LPM problems and prove the convergence properties of these algorithms. 相似文献
9.
The purpose of this paper is to discuss those kinds of statistical convergence,in terms of filter F,or ideal L-convergence,which are equivalent to measure convergence defined by a single statistical measure.We prove a number of characterizations of a single statistical measure μ-convergence by using properties of its corresponding quotient Banach space l_∞/l_∞(I_μ).We also show that the usual sequential convergence is not equivalent to a single measure convergence. 相似文献
10.
James G. Hooton 《Journal of Mathematical Analysis and Applications》1981,83(2):570-581
We provide conditions on a finite measure μ on n which insure that the imbeddings Wk, p(ndμ)?Lp(ndμ) are compact, where 1 ? p < ∞ and k is a positive integer. The conditions involve uniform decay of the measure μ for large ¦x¦ and are satisfied, for example, by . 相似文献
11.
Shuenn-Ren Cheng 《Journal of Mathematical Analysis and Applications》2009,353(2):531-543
In this paper we consider the highly nonlinear model in finance proposed by Ait-Sahalia [Y. Ait-Sahalia, Testing continuous-time models of the spot interest rate, Rev. Finan. Stud. 9 (2) (1996) 385-426]. Both the drift and diffusion coefficients in this model do not obey the classical linear growth condition. To overcome the difficulties due to the highly nonlinear coefficients, we develop several new techniques to study the analytical properties of the model including the positivity and boundedness. In particular, we show that the Euler-Maruyama approximate solutions converge to the true solution in probability. The convergence result justifies clearly that the Monte Carlo simulations based on the Euler-Maruyama scheme can be used to compute the expected payoff of financial products e.g. options. 相似文献
12.
Monika Remy 《manuscripta mathematica》1988,62(3):277-296
For every finite measure space (X,A,P) we find a unique representation P=Q1+Q2+Q3 such that Q1 is compact, Q2 is perfect and purely noncompact and Q3 is purely nonperfect. We show that every Pachl-O-disintegrable probability space is Ramachandran-O-disintegrable and therefore perfect and under a certain condition we prove the equivalence between compactness and Ramachandran-O-disintegrability. 相似文献
13.
Positivity - In this paper we investigate the distance of convergence in measure whenever the measure is not $$sigma $$ -finite and identify the topological coreflection of this approach structure... 相似文献
14.
Let(Ω,Σ,μ)be a complete probability space and let X be a Banach space.We introduce the notion of scalar equi-convergence in measure which being applied to sequences of Pettis integrable functions generates a new convergence theorem.We also obtain a Vitali type I-convergence theorem for Pettis integrals where I is an ideal on N. 相似文献
15.
《Mathematische Nachrichten》2017,290(17-18):3020-3028
Let X be a measurable space, let be a family of measurable subsets of it, and let be a subspace of complex measures on X that is also closed under restrictions of measures. In this paper we introduce the ‐convergence topology and the ‐strict topology on . Among other results, we find necessary and sufficient conditions for Hausdorff‐ness and coincide‐ness of these topologies. Applications to Lebesgue spaces, and also examples in Hausdorff topological spaces and locally compact groups are given. 相似文献
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17.
We prove that the probabilistic norms of suitable Probabilistic Normed spaces induce convergence in probability, Lp convergence and almost sure convergence. 相似文献
18.
David R. Stockman 《Applicable analysis》2013,92(2):293-299
19.
A representation of the characteristic function of a stable probability measure on certain TV spaces
Balram S. Rajput 《Journal of multivariate analysis》1976,6(4):592-600
In this paper, a Lévy-Khintchine type representation of the characteristic function of a K-regular stable probability measure on real locally convex topological vector spaces, satisfying certain conditions, is presented. 相似文献
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