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	Law of the iterated logarithm - Wikipedia, the free encyclopedia
		In probability theory, the law of the iterated logarithm is the name given to several theorems which describe the magnitude of the fluctuations of a random walk.
		The original statement (1924) of the law of the iterated logarithm is due to A.
		One of the simpler forms of the law of the iterated logarithm can be stated as follows (Theorem 3.52 in Breiman).
	en.wikipedia.org /wiki/Law_of_the_iterated_logarithm (176 words)

	Some effects of trimming on the law of the iterated logarithm, Harry Kesten, Ross Maller
		Hartman, P. and Wintner, A. On the law of the iterated logarithm.
		Maller, R. A functional law of the iterated logarithm for distributions in the domain of partial attraction of the normal distribution.
		Strassen, V. A converse to the law of the iterated logarithm.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.jap/1082552203 (508 words)

	Iterated logarithm - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-26)
		is often used to indicate the binary iterated logarithm, which iterates the binary logarithm instead.
		The iterated logarithm is useful in analysis of algorithms and their computational complexity, appearing in the time and space complexity bounds of many algorithms such as:
		For all practical purposes, the iterated logarithm may be considered to be a constant.
	en.wikipedia.org /wiki/Iterated_logarithm (322 words)

	Rodrigo Bañuelos Professor of Mathematics : Publications.html
		An analogue for harmonic functions of Kolmogorov's law of the iterated logarithm.
		Laws of the iterated logarithm, sharp good-λ inequalities and L p-estimates for caloric and harmonic functions.
		The lower bound in the law of the iterated logarithm for harmonic functions.
	www.math.purdue.edu /~banuelos/site/Publications.html (751 words)

	A Law Of The Iterated Logarithm For Stable Processes In Random Scenery - Khoshnevisan, Lewis (ResearchIndex)
		We prove a law of the iterated logarithm for stable processes in a random scenery.
		Brownian motion in stable scenery; law of the iterated logarithm; quasi-- association 1991 Mathematics Subject Classification.
		Khoshnevisan, D. and Lewis, T.M. (1998) A law of the iterated logarithm for stable processes in random scenery.
	citeseer.ist.psu.edu /khoshnevisan98law.html (744 words)

	The Law of the Iterated . . . (ResearchIndex) (Site not responding. Last check: 2007-10-26)
		Abstract: : We study the compact law of the iterated logarithm for a certain type of triangular arrays of empirical processes, appearing in statistics (M--estimators, regression, density estimation, etc).
		We give necessary and sufficient conditions for the law of the iterated logarithm of these processes of the type of conditions used in Ledoux and Talagrand (1991): convergence in probability, tail conditions and total boundedness of the parameter space with respect to certain pseudometric.
		25 the law of the iterated logarithm for canonical U--statistic..
	citeseer.ist.psu.edu /184950.html (443 words)

	On Large Random Graphs of the ‘Internet Type
		The length of the paths between typical nodes grows very slowly, as the iterated logarithm (log log) of the number of nodes.
		We investigated the same model without cutoff and proved that the average distance is at most of the order of the iterated logarithm of the number of nodes.
		For instance, at value 3 the diameter of the graph changes from logarithmic to iterated logarithm between values 2 and 3, and finally below 2 the diameter is essentially bounded.
	www.ercim.org /publication/Ercim_News/enw50/reittu.html (1197 words)

	Mary Weiss Abstract (Site not responding. Last check: 2007-10-26)
		The purpose of this paper is to prove the following theorem of "The Law of the Iterated Logarithm" for lacunary trigonometric series.
		The Law of the Iterated Logarithm for lacunary series has already been treated in the literature.
		In the proof which follows we use some ideas from these two papers and also from the classical paper of Kolmogoroff on the Law of the Iterated Logarithm for independent random variables.
	www.agnesscott.edu /LRiddle/women/abstracts/weiss_abstract.htm (173 words)

	M. Arcones' publications
		The law of the iterated logarithm for U-processes.
		On the law of the iterated logarithm for canonical U-statistics and processes.
		The law of the iterated logarithm for a triangular array of empirical processes.
	www.math.binghamton.edu /arcones/public.html (649 words)

	Electronic Journal of Probability - Vol. 2 (1997) (Site not responding. Last check: 2007-10-26)
		We study the compact law of the iterated logarithm for a certain type of triangular arrays of empirical processes, appearing in statistics (M-estimators, regression, density estimation, etc).
		As an application, we consider the law of the iterated logarithm for a class of density estimators.
		We also consider the compact law of the iterated logarithm for kernel density estimators when they have large deviations similar to those of a Poisson process.
	www.math.washington.edu /~ejpecp/viewarticle.php?id=1221 (439 words)

	Untitled Document
		Kaufman, R. and Philipp, W. A uniform law of the iterated logarithm for classes of functions.
		Stout, W. The law of the iterated logarithm and upper lower class test for partial sums of stationary Gaussian sequences, Ann.
		Philipp, W. A functional law of the iterated logarithm for empirical distribution functions of weakly dependent random variables.
	www.stat.uiuc.edu /research/prior1980.html (1495 words)

	Earliest Known Uses of Some of the Words of Mathematics (L) (Site not responding. Last check: 2007-10-26)
		It undoubtedly was Napier's observation that logarithms of proportionals are "equidifferent" that led him to coin the name "logarithm," which occurs throughout the Descriptio but only in the title of the Constructio, which clearly was drafted first although published later.
		Logarithm appears in English in 1616 in E. Wright's English translation of the Descriptio: "This new course of Logarithmes doth cleane take away all the difficultye that heretofore hath beene in mathematicall calculations.
		Logarithmic curve is found in English in 1715 in The Elements of Astronomy, Physical and Geometrical by David Gregory and Edmond Halley: "But this is the Property of the Logarithmic Curve very well known to Geometricians; therefore the Curve ACX is a Logarithmic Curve, whose Asymptote is the Right line BZ.
	hometown.aol.com /jeff570/l.html (7204 words)

	Springer Online Reference Works
		is a sequence of numbers, the theorem on the law of the iterated logarithm deals with sequences of numbers
		Feller [4] examined a generalization of Kolmogorov's law of the iterated logarithm for sequences of independent bounded non-identically distributed random variables.
		The results obtained on the law of the iterated logarithm for sequences of independent random variables have served as a starting point for numerous researches on the applicability of this law to sequences of dependent random variables and vectors and to random processes.
	eom.springer.de /L/l057740.htm (430 words)

	Institute of Mathematics of National Academy of Sciences of Armenia (Site not responding. Last check: 2007-10-26)
		Gasparian, The iterated logarithm laws for optional martingales, pp.
		The paper presents a characterization of the set of convergence for optional local martingales in (strong) predictable terms, extending to the optional case the facts received by Yu.
		The iterated logarithm laws for local and locally square--integrable optional martingales are obtained.
	math.sci.am /Journal/1994_3.html (357 words)

	The law of the iterated logarithm for the multivariate kernel mode estimator (Site not responding. Last check: 2007-10-26)
		The law of the iterated logarithm for the multivariate kernel mode estimator
		Then, we obtain a multivariate law of the iterated logarithm for the kernel mode estimator by proving that, with probability one, the limit set of the sequence
		Key words: Density, mode, kernel estimator, central limit theorem, law of the iterated logarithm.
	www.edpsciences.org /articles/ps/abs/2003/01/ps120/ps120.html (154 words)

	Publications of Jay S. Rosen (1991-1996) (Site not responding. Last check: 2007-10-26)
		Logarithmic averages for the local times of recurrent random walks and Levy processes, (with M. Marcus), Stoch.
		Laws of the iterated logarithm for the local times of symmetric Levy processes and recurrent random walks, (with M. Marcus), Annals of Probability, 22 (1994), 620-659.
		Laws of the iterated logarithm for the local times of recurrent random walks on Z^2 and of Levy processes and recurrent random walks in the domain of attraction of Cauchy random variables, (with M. Marcus).
	www.library.csi.cuny.edu /dept/math/jrosen/pub9196.html (420 words)

	Self-normalized processes: exponential inequalities, moment bounds and iterated logarithm laws, Victor H. de la ... (Site not responding. Last check: 2007-10-26)
		In this paper we present several exponential and moment inequalities, particularly those related to laws of the iterated logarithm, for self-normalized random variables including martingales.
		Another development in this paper is a bounded law of the iterated logarithm for general adapted sequences that are centered at certain truncated conditional expectations and self-normalized by the square root of the sum of squares.
		A compact law of the iterated logarithm for self-normalized martingales is also derived in this connection.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.aop/1089808415 (652 words)

	ON HARTMAN'S LAW OF ITERATED LOGARITHM FOR EXPLOSIVE GAUSSIAN AUTOREGRESSIVE PROCESSES (Site not responding. Last check: 2007-10-26)
		On établit une loi du logarithme itéré pour l'estimateur du maximum de vraisemblance du paramètre inconnu d'un processus autorégressif gaussien explosif.
		A law of iterated logarithm is established for the maximum likelihood estimator of the unknown parameter of the explosive Gaussian autoregressive process.
		Outside the Gaussian case, we show that the law of iterated logarithm does not hold, except for a suitable averaging on the maximum likelihood estimator.
	www.math.u-psud.fr /~biblio/ppo/2001/ppo2001-04.html (149 words)

	List of publications
		Large deviations and law of the iterated logarithm for partial sums normalized by the largest absolute observation.
		A Chung type law of the iterated logarithm for subsequences of a Wiener process.
		The law of the iterated logarithm for negatively associated random variables.
	darkwing.uoregon.edu /~qmshao/pub/pub.htm (1401 words)

	[No title]
		On the law of the iterated logarithm for canonical U-statistics and U-processes.
		A law of the iterated logarithm for kernel density estimators in the presence of censoring.
		The law of the iterated logarithm for the integrated squared deviation of a kernel density estimator.
	www.math.uconn.edu /~gine/Publications/index.html (944 words)

	Publications of Michael B. Marcus (1991-1999) (Site not responding. Last check: 2007-10-26)
		Laws of the iterated logarithm for intersections of random walks in Z^4, (with J. Rosen), Ann.
		Logarithmic averages for the local times of recurrent random walks and Levy processes, (with J. Rosen), Stoch.
		Laws of the iterated logarithm for the local times of recurrent random walks on Z^2 and of Levy processes and recurrent random walks in the domain of attraction of Cauchy random variables, (with J. Rosen), Ann.
	home.earthlink.net /~mbmarcus/pub9199.html (544 words)

	Publications 1991-1999
		A generalization of Chung-Mogul'skii law of the iterated logarithm.
		On the Spitzer and Chung laws of the iterated logarithm for Brownian motion.
		The Csörgö-Révész modulus of non-differentiability of iterated Brownian motion.
	www.proba.jussieu.fr /pageperso/zhan/pub91-99.html (579 words)

	Letter L
		From this follows the law of iterated logarithm of Russian probabilist, A. Khinchine.
		It follows that the probability law of the iterated logarithm translates into a similar law for verdibility.
		Unlike the finitary integral vector of naturals and the finitary rational vector of integers, this requires infinite vectors derived from Cauchy sequences of rationals known as "decimal numbers".
	members.fortunecity.com /jonhays/letterL.htm (1112 words)

	UvT: John H.J. Einmahl
		A general form of the law of the iterated logarithm for the weighted multivariate empirical process (1987).
		Laws of the iterated logarithm in the tails for weighted uniform empirical processes (1988).
		The functional law of the iterated logarithm for the empirical process based on sample means (2001).
	center.uvt.nl /staff/einmahl (928 words)

	ECP Vol 8, Paper 7 (Abstract) (Site not responding. Last check: 2007-10-26)
		For a sequence of independent identically distributed Euclidean random vectors, we prove a law of the iterated logarithm for the sample covariance matrix when o(log log n) terms are omitted.
		The result is proved under the hypothesis that the random vectors belong to the generalized domain of attraction of the multivariate Gaussian law.
		As an application, we obtain a bounded law of the iterated logarithm for the multivariate t-statistic.
	www.maths.tcd.ie /EMIS/journals/EJP-ECP/EcpVol8/paper7.abs.html (112 words)

	The Law of the Iterated Logarithm for a Triangular Array of Empirical Processes - Arcones (ResearchIndex)
		The Law of the Iterated Logarithm for a Triangular Array of Empirical Processes (1997)
		Arcones, M. The law of the iterated logarithm for a triangular array of empirical processes.
		@misc{ arcones94law, author = "M. Arcones", title = "The law of the iterated logarithm for a triangular array of empirical processes", text = "Arcones, M. The law of the iterated logarithm for a triangular array of empirical processes.
	citeseer.ist.psu.edu /274451.html (586 words)

	Deng's home page
		In the meantime, I focus the research on probability limit theory such as law of large number, central limit theorem, law of iterated logarithm, and the convergence rate estimates in real and Banach space valued random variables.
		Wittmann's Law of Iterated Logarithm of Tail Sums for $B$-Valued Random Variables, J. Theo.
		On the self-normalized bounded laws of iterated logarithm in Banach space, Stat.
	www.math.uregina.ca /~deng (217 words)

	\bf BIBLIOGRAPHY
		R.F. Bass and R. Pyke, Functional law of the iterated logarithm and uniform central limit theorem for partial-sum processes indexed by sets, Ann.
		R.F. Bass and K.B. Erickson, Local laws of the iterated logarithm for diffusions, Ann.
		R.F. Bass and T. Kumagai, Laws of the iterated logarithm for the range of random walks in two and three dimensions, Ann.
	www.math.uconn.edu /~bass/biblio.html (1831 words)

	Ver%ouml;ffentlichung von Hans-Peter Scheffler
		A law of the iterated logarithm for randomly stopped sums of heavy tailed random vectors, Monatshefte Mathematik, Vol.
		A law of the iterated logarithm for semistable laws on vector spaces and homogeneous groups, Journal of Mathematical Science, Vol.
		Laws of the iterated logarithm for the central part of (semi-)stable measures on the Heisenberg group, Monatshefte Mathematik, Vol.
	www.mathematik.uni-dortmund.de /lsiv/scheffler/hps_litt.html (540 words)

	DC MetaData for: Some problems related to the functional law of the iterated logarithm
		The law of the iterated logarithm is one of the most important
		the functional law of the iterated logarithm for the increments of
		The author(s) agree, that this abstract may be stored as full text and distributed as such by abstracting services.
	www.minet.uni-jena.de /Math-Net/reports/shadows/99-33report.html (217 words)

	Amazon.co.uk: Iterated: Books (Site not responding. Last check: 2007-10-26)
		Iterated Nonlinear Maps and Hilbert's Projective Metric, II (Memoirs of the American Mathematical Society) by Roger D. Nussbaum (Paperback - 2 Jul 1992)
		Iterated Integrals and Cycles on Algebraic Manifolds (Iterated Integrals and Cycles on Algebraic Manifolds (Nankai Tracts in Mathematics: Vol.
		Iterated Inductive Definitions and Subsystems of Analysis: 897 (Lecture Notes in Mathematics, Vol 897) by Wilfried Buchholz (Paperback - April 1982)
	www.amazon.co.uk /s?ie=UTF8&keywords=Iterated&tag=booksandvideo&index=books-uk&link_code=qs&page=1 (358 words)

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