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• "limit laws"
Clear All  # Spacings-ratio empirical processes

Periodica Mathematica Hungarica
Authors: Paul Deheuvels and Gérard Derzko

## Abstract

We consider an empirical process based upon ratios of selected pairs of spacings, generated by independent samples of arbitrary sizes. As a main result, we show that when both samples are uniformly distributed on (possibly shifted) intervals of equal lengths, this empirical process converges to a mean-centered Brownian bridge of the form B C(u) = B(u)−6Cu(1−u) Σ0 1 B(s)ds, where B(·) denotes a Brownian bridge, and C, a constant. The investigation of the class of Gaussian processes {B C(·): C ∈ ℝ} leads to some unexpected distributional identities such as B 2(·)

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\underline{\underline d}$$ \end{document}
B(·). We discuss this and similar results in an extended framework.

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# Penalizing a BES ( d ) process (0 < d < 2) with a function of its local time, V

Studia Scientiarum Mathematicarum Hungarica
Authors: Bernard Roynette, Pierre Vallois and Marc Yor

We describe the limit laws, as t → ∞, of a Bessel process ( R s , st ) of dimension d ∈ (0, 2) penalized by an integrable function of its local time L t at 0, thus extending our previous work of this kind, relative to Brownian motion.

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# Weak convergence of random walks, conditioned to stay away from small sets

Studia Scientiarum Mathematicarum Hungarica
Authors: Zsolt Pajor-Gyulai and Domokos Szász

Let {X n}n∈ℕ be a sequence of i.i.d. random variables in ℤd. Let S k = X 1 + … + X k and Y n(t) be the continuous process on [0, 1] for which Y n(k/n) = S k/n 1/2 for k = 1, … n and which is linearly interpolated elsewhere. The paper gives a generalization of results of () on the weak limit laws of Y n(t) conditioned to stay away from some small sets. In particular, it is shown that the diffusive limit of the random walk meander on ℤd: d ≧ 2 is the Brownian motion.

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# A law of the single logarithm for moving averages of random variables under exponential moment conditions

Studia Scientiarum Mathematicarum Hungarica
Author: H. Lanzinger

9 20 SHEPP, L. A., A limit law concerning moving averages, Ann. Math. Stat . 35 (1964), 424-428. MR 29 #4091 A limit law concerning moving

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# One-sided strong laws forincrements of sumsof i.i.d. random variables

Studia Scientiarum Mathematicarum Hungarica
Author: A. N. Frolov

DEHEUVELS, P. and DEVROYE, L., Limit laws of Erdős-Rényi-Shepp type, Ann. Probab. 15 (1987), 1363-1386. MR 88f :60055 Limit laws of Erdős-Rényi-Shepp type

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# Conditions for equivalence between Mallows distance and convergence to stable laws

Acta Mathematica Hungarica
Authors: Chang C. Y. Dorea and Debora B. Ferreira

] Mijnheer , J. 1986 On the rate of convergence to a stable limit law II Litovsk. Mat. Sb. 26 482 – 487 . [10

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# Central limit theorems for logarithmic averages

Studia Scientiarum Mathematicarum Hungarica
Authors: I. Berkes, L. Horváth and X. Chen

. 104 561 574 CHEN, X., On the limit laws of the second order for additive functionals of Harris recurrent Markov chains, Probab. Theory Related

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# Convergence of multivalued mils and pramarts in spaces without the RNP

Studia Scientiarum Mathematicarum Hungarica
Author: G. Krupa

Artstein, Z. and Hansen, J. C., Convexification in limit laws of random sets in Banach spaces, Ann. Probab. 13 (1985), 307-309. MR 86e :60008 Convexification in limit laws of random

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# On the asymptotic joint distribution of height and width in random trees

Studia Scientiarum Mathematicarum Hungarica
Author: Svante Janson

{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \int_0^1 {\tfrac{{ds}}{{r(s)}}\mathop = \limits^{(law)} 2\sup _{s \leqq 1

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