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Journal of Theoretical Probability - Let $$ \{X, X_{n};~n \ge 1 \}$$ be a sequence of independent and identically distributed Banach space valued random variables. This paper is devoted to... 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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We study the almost sure limiting behavior and convergence in probability of weighted partial sums of the form
where {Wnj, 1jn, n1} and {Xnj, 1jn, n1} are triangular arrays of random variables. The results obtain irrespective of the joint distributions of the random variables within each array. Applications concerning the Efron bootstrap and queueing theory are discussed. 相似文献
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Lennart R. Flood Mercedes C. Rosalsky Henri Theil 《Statistics & probability letters》1984,2(4):187-191
Simulations based on two sets of data are used to assess the impact of combining equations on the accuracy of parameter estimates and their asymptotic standard errors. 相似文献
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De Li LI Andrew ROSALSKY Andrei VOLODIN 《数学学报(英文版)》2007,23(4):599-612
For a sequence of i.i.d. Banach space-valued random variables {Xn; n ≥ 1} and a sequence of positive constants {an; n ≥ 1}, the relationship between the Baum-Katz-Spitzer complete convergence theorem and the law of the iterated logarithm is investigated. Sets of conditions are provided under which
(i) lim sup n→∞ ||Sn||/an〈∞ a.s.and
∞ ∑n=1(1/n)P(||Sn||/an ≥ε〈∞for all ε 〉 λ for some constant λ ∈ [0, ∞) are equivalent;
(ii) For all constants λ ∈ [0, ∞),
lim sup ||Sn||/an =λ a.s.and ^∞∑ n=1(1/n) P(||Sn||/an ≥ε){〈∞, if ε〉λ =∞,if ε〈λare equivalent. In general, no geometric conditions are imposed on the underlying Banach space. Corollaries are presented and new results are obtained even in the case of real-valued random variables. 相似文献
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Andrew Rosalsky 《Probability Theory and Related Fields》1981,58(3):351-372
Summary A generalization of the classical Law of the Iterated Logarithm (LIL) is obtained for the weighted i.i.d. case consisting of sequences {
n
Y
n
} where the weights {
n
} are nonzero constants and {Y
n} are i.i.d. random variables. If Y is symmetric but not necessarily square integrable and if the weights satisfy a certain growth rate, conditions are given which guarantee that {
n
Y
n} obey a Generalized Law of the Iterated Logarithm (GLIL) in the sense that
almost certainly for some positive conslants a
n
. Teicher has shown that such weights entail the classical LIL when EY
2< and Feller has treated the GLIL when
n
=1 and EY
2=. The main finding here asserts that if {qn} satisfies q
n
2
=nG(qn)loglogq
n
where G is a specified slowly varying function, asymptotically equivalent to the truncated second moment of Y, and if a certain series converges, then the GLIL obtains with
where
. 相似文献