Results 11 to 20 of about 2,873 (97)
A semicircle law and decorrelation phenomena for iterated Kolmogorov loops
Journal of the London Mathematical Society, Volume 103, Issue 2, Page 558-586, March 2021., 2021 Abstract We consider a standard one‐dimensional Brownian motion on the time interval [0,1] conditioned to have vanishing iterated time integrals up to order N. We show that the resulting processes can be expressed explicitly in terms of shifted Legendre polynomials and the original Brownian motion, and we use these representations to prove that the ...
Karen Habermann
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Precise lim sup behavior of probabilities of large deviations for sums of i.i.d. random variables
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 66, Page 3565-3576, 2004., 2004 Let {X, Xn; n ≥ 1} be a sequence of real‐valued i.i.d. random variables and let Sn=∑i=1nXi, n ≥ 1. In this paper, we study the probabilities of large deviations of the form P(Sn > tn1/p), P(Sn < −tn1/p), and P(|Sn| > tn1/p), where t > 0 and 0 < p < 2.
Deli Li, Andrew Rosalsky
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Open Mathematics, 2020 In this article, an errors-in-variables regression model in which the errors are negatively superadditive dependent (NSD) random variables is studied. First, the Marcinkiewicz-type strong law of large numbers for NSD random variables is established. Then,
Zhang Yu +3 more
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On multiple‐particle continuous‐time random walks
Journal of Applied Mathematics, Volume 2004, Issue 3, Page 213-233, 2004., 2004 Scaling limits of continuous‐time random walks are used in physics to model anomalous diffusion in which particles spread at a different rate than the classical Brownian motion. In this paper, we characterize the scaling limit of the average of multiple particles, independently moving as a continuous‐time random walk.
Peter Becker-Kern, Hans-Peter Scheffler
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Cauchy approximation for sums of independent random variables
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 17, Page 1055-1066, 2003., 2003 We use Stein′s method to find a bound for Cauchy approximation. The random variables which are considered need to be independent.
K. Neammanee
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A zero‐inflated occupancy distribution: exact results and Poisson convergence
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 28, Page 1771-1782, 2003., 2003 We introduce the generalized zero‐inflated allocation scheme of placing n labeled balls into N labeled cells. We study the asymptotic behavior of the number of empty cells when (n, N) belongs to the “right” and “left” domain of attraction. An application to the estimation of characteristics of agreement among a set of raters which independently ...
Nikolai Kolev, Ljuben Mutafchiev
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A nonuniform bound for the approximation of Poisson binomial by Poisson distribution
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 48, Page 3041-3046, 2003., 2003 It is well known that Poisson binomial distribution can be approximated by Poisson distribution. In this paper, we give a nonuniform bound of this approximation by using Stein‐Chen method.
K. Neammanee
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A survey of limit laws for bootstrapped sums
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 45, Page 2835-2861, 2003., 2003 Concentrating mainly on independent and identically distributed (i.i.d.) real‐valued parent sequences, we give an overview of first‐order limit theorems available for bootstrapped sample sums for Efron′s bootstrap. As a light unifying theme, we expose by elementary means the relationship between corresponding conditional and unconditional bootstrap ...
Sándor Csörgő, Andrew Rosalsky
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Central limit theorem for an additive functional of the fractional Brownian motion II [PDF]
, 2013 We prove a central limit theorem for an additive functional of the $d$-dimensional fractional Brownian motion with Hurst index $H\in(\frac{1}{2+d},\frac{1}{d})$, using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in ...
Nualart, David, Xu, Fangjun
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Almost sure central limit theorems for strongly mixing and associated random variables
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 3, Page 125-131, 2002., 2002 We prove an almost sure central limit theorem (ASCLT) for strongly mixing sequence of random variables with a slightly slow mixing rate α(n) = O((loglogn)−1−δ). We also show that ASCLT holds for an associated sequence of random variables without a stationarity assumption.
Khurelbaatar Gonchigdanzan
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