Results 21 to 30 of about 105 (105)
International Journal of Stochastic Analysis, Volume 14, Issue 1, Page 27-46, 2001., 2001 This paper establishes the rate of convergence (in the uniform Kolmogorov distance) for normalized additive functionals of stochastic processes with long‐range dependence to a limiting Rosenblatt distribution.
N. N. Leonenko, V. V. Anh
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On the approximation of an integral by a sum of random variables
International Journal of Stochastic Analysis, Volume 11, Issue 2, Page 107-114, 1998., 1997 We approximate the integral of a smooth function on [0, 1], where values are only known at n random points (i.e., a random sample from the uniform‐(0, 1) distribution), and at 0 and 1. Our approximations are based on the trapezoidal rule and Simpson′s rule (generalized to the non‐equidistant case), respectively.
John H. J. Einmahl +1 more
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Lifetime Distributions and their Approximation in Reliability of Serial/Parallel Networks
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 In this paper we present limit theorems for lifetime distributions connected with network’s reliability as distributions of random variables(r.v.) min(Y1, Y2,..., YM) and max(Y1, Y2,..., YM ), where Y1, Y2,..., are independent, identically distributed ...
Leahu Alexei +1 more
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International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 3, Page 443-450, 1997., 1996 The convergence in mean of a weighted sum ∑kank(Xk − EXk) of random elements in a separable Banach space is studied under a new hypothesis which relates the random elements with their respective weights in the sum: the {ank}‐compactly uniform integrability of {Xn}.
M. Ordóñez Cabrera
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International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 3, Page 441-450, 1996., 1995 In this paper a uniform estimate is obtained for the remainder term in the central limit theorem (CLT) for a sequence of random vectors forming a homogeneous Markov chain with arbitrary set of states. The result makes it possible to estimate the rate of convergence in the CLT without assuming the finiteness of the absolute third moment of the ...
M. Gharib
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Nonparametric density estimators based on nonstationary absolutely regular random sequences
International Journal of Stochastic Analysis, Volume 9, Issue 3, Page 233-254, 1996., 1995 In this paper, the central limit theorems for the density estimator and for the integrated square error are proved for the case when the underlying sequence of random variables is nonstationary. Applications to Markov processes and ARMA processes are provided.
Michel Harel, Madan L. Puri
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On Feller′s criterion for the law of the iterated logarithm
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 2, Page 323-340, 1994., 1993 Combining Feller′s criterion with a non‐uniform estimate result in the context of the Central Limit Theorem for partial sums of independent random variables, we obtain several results on the Law of the Iterated Logarithm. Two of these results refine corresponding results of Wittmann (1985) and Egorov (1971). In addition, these results are compared with
Deli Li, M. Bhaskara Rao, Xiangchen Wang
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asymptotics for open‐loop window flow control
International Journal of Stochastic Analysis, Volume 7, Issue 3, Page 337-356, 1994., 1993 An open‐loop window flow‐control scheme regulates the flow into a system by allowing at most a specified window size W of flow in any interval of length L. The sliding window considers all subintervals of length L, while the jumping window considers consecutive disjoint intervals of length L.
Arthur W. Berger, Ward Whitt
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Global Central Limit Theorems for Stationary Markov Chains
Annales Mathematicae SilesianaeLet P be a Markov operator on a general state space (S, Σ) with an invariant probability measure m, assumed to be ergodic. We study conditions which yield that for every centered non-zero f ∈ L2(m) a non-degenerate annealed CLT and an L2-normalized CLT ...
Lin Michael
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On the weak law of large numbers for normed weighted sums of I.I.D. random variables
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 1, Page 191-202, 1991., 1991 For weighted sums of independent and identically distributed random variables {Yn, n ≥ 1}, a general weak law of large numbers of the form is established where {νn, n ≥ 1} and {bn, n ≥ 1} are statable constants. The hypotheses involve both the behavior of the tail of the distribution of |Y1| and the growth behaviors of the constants {an, n ≥ 1} and {bn,
André Adler, Andrew Rosalsky
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