共查询到20条相似文献,搜索用时 15 毫秒
1.
Makoto Maejima 《Journal of Theoretical Probability》1993,6(1):57-69
Limit laws for trimmed sums of triangular arrays of i.i.d. Banach space valued random variables are studied. It is shown that if the array belongs to the domain of attraction of an infinitely divisible law without Gaussian component on a separable Banach space of type 2, then the trimmed sum converges weakly to a nondegenerate Banach space valued random variable. 相似文献
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Periodica Mathematica Hungarica - Let X 1,X 2,... be a sequence of independent and identically distributed random variables, and put % MATHTYPE!MTEF!2!1!+-%... 相似文献
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Let be a sequence of i.i.d. random vectors with values in a separable Banach space. Moderate deviation principles for trajectories of sums of are proved, which generalize related results of Borovkov and Mogulskii (1980) and Deshayes and Picard (1979). As an application, functional laws of the iterated logarithm are given. The paper also contains concluding remarks, with examples, on extending results for partial sums to corresponding ones for trajectory setting.
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Let F be a Banach space with a sufficiently smooth norm. Let (Xi)i≤n be a sequence in LF2, and T be a Gaussian random variable T which has the same covariance as X = Σi≤nXi. Assume that there exists a constant G such that for s, δ≥0, we have P(sTs+δ)Gδ. (*) We then give explicit bounds of Δ(X) = supi|P(|X|≤t)−P(|T|≤t)| in terms of truncated moments of the variables Xi. These bounds hold under rather mild weak dependence conditions of the variables. We also construct a Gaussian random variable that violates (*). 相似文献
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A. V. Lebedev 《Mathematical Notes》2005,77(3-4):503-509
A general scheme of maxima of sums of independent random variables is introduced. We prove a theorem on the convergence of the maxima in probability. We study its applications to large jumps in random walks and to extrema of shot-noise fields in the case of regularly varying tails. Nondegenerate limiting laws are obtained.Translated from Matematicheskie Zametki, vol. 77, no. 4, 2005, pp. 544–550.Original Russian Text Copyright © 2005 by A. V. Lebedev.This revised version was published online in April 2005 with a corrected issue number. 相似文献
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The purpose of this paper is to show the equivalence of almost sure convergence of Sn/n, n ≥ 1 and lim supn→∞Sn/n < ∞ a.e., where Sn = X1 + X2 + … + Xn and X1, X2,… are independent identically distributed random elements in a separable Banach space with EX1 < ∞. This result disproves a result of Pop-Stojanovic [8]. 相似文献
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For a double array of independent random elements {Vmn,m ≥ 1,n ≥ 1} in a real separable Banach space,conditions are provided under which the weak and strong laws of large numbers for the double sums mi=1 nj=1Vij,m ≥ 1,n ≥ 1 are equivalent.Both the identically distributed and the nonidentically distributed cases are treated.In the main theorems,no assumptions are made concerning the geometry of the underlying Banach space.These theorems are applied to obtain Kolmogorov,Brunk–Chung,and Marcinkiewicz–Zygmund type strong laws of large numbers for double sums in Rademacher type p(1 ≤ p ≤ 2) Banach spaces. 相似文献
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In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes. 相似文献
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Gregory Beylkin Lucas Monzón Ignas Satkauskas 《Applied and Computational Harmonic Analysis》2019,46(2):400-416
We introduce a new functional representation of probability density functions (PDFs) of non-negative random variables via a product of a monomial factor and linear combinations of decaying exponentials with complex exponents. This approximate representation of PDFs is obtained for any finite, user-selected accuracy. Using a fast algorithm involving Hankel matrices, we develop a general numerical method for computing the PDF of the sums, products, or quotients of any number of non-negative independent random variables yielding the result in the same type of functional representation. We present several examples to demonstrate the accuracy of the approach. 相似文献
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MIAO Yu & MU JianYong College of Mathematics Information Science Henan Normal University Xinxiang China 《中国科学 数学(英文版)》2011,(4)
Let(Xn)n≥1 be a sequence of independent identically distributed(i.i.d.) positive random variables with EX1 = μ,Var(X1) = σ2.In the present paper,we establish the moderate deviations principle for the products of partial sums(Πnk=1Sk/n!μn)1/(γbn√(2n))1where γ = σ/μ denotes the coefficient of variation and(bn) is the moderate deviations scale. 相似文献
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A limit of a sequence of fuzzy numbers is defined and its some properties are shown. Based on these concept and properties, an independent sequence of fuzzy random variables is considered and a strong law of large numbers for fuzzy random variables is shown. 相似文献
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In this paper, Kolmogorov's strong law of large numbers for sums of independent and level-wise identically distributed fuzzy random variables is obtained. 相似文献
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For weighted sums Σj = 1najVj of independent random elements {Vn, n ≥ 1} in real separable, Rademacher type p (1 ≤ p ≤ 2) Banach spaces, a general weak law of large numbers of the form (Σj = 1najVj − vn)/bn →p 0 is established, where {vn, n ≥ 1} and bn → ∞ are suitable sequences. It is assumed that {Vn, n ≥ 1} is stochastically dominated by a random element V, and the hypotheses involve both the behavior of the tail of the distribution of |V| and the growth behaviors of the constants {an, n ≥ 1} and {bn, n ≥ 1}. No assumption is made concerning the existence of expected values or absolute moments of the {Vn, n >- 1}. 相似文献
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J Kuelbs 《Journal of multivariate analysis》1973,3(2):161-172
We extend the invariance principle to triangular arrays of Banach space valued random variables, and as an application derive the invariance principle for lattices of random variables. We also point out how the q-dimensional time parameter Yeh-Wiener process is naturally related to a one dimensional time Wiener process with an infinite dimensional Banach space as a state space. 相似文献
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In this paper, we obtain sample path and scalar large deviation principles for the product of sums of positive random variables. We study the case when the positive random variables are independent and identically distributed and bounded away from zero or the left tail decays to zero sufficiently fast. The explicit formula for the rate function of a scalar large deviation principle is given in the case when random variables are exponentially distributed. 相似文献
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Leonid Rozovsky 《Statistics & probability letters》2012,82(1):72-76
In the note we study large and superlarge deviation probabilities of sum of i.i.d. lattice random variables, whose distribution function has an exponentially decreasing tail at infinity. 相似文献