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Topic: Law of the iterated logarithm

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	[No title]
		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. Ya.
		Figure 3.19 shows the logarithm of macroscopic permeability versus the logarithm of formation factor from numerical simulations of a hypothetical rough-walled fracture generated by using rough surfaces of fractal dimension D = 2.5 (Brown, 1989).
	www.lycos.com /info/logarithm.html (613 words)

	The Law of the Iterated Logarithm for a Trianglar Array of Empirical Processes (ResearchIndex)
		25 the law of the iterated logarithm for canonical U--statistic..
		22 Laws of the iterated logarithm for nonparametric density est..
		21 A law of the iterated logarithm for nonparametric regression..
	citeseer.ist.psu.edu /676.html (460 words)

	Strong approximation of quantile processes by iterated Kiefer processes
		The notion of a $k$th iterated Kiefer process $\mathscr{K}(v,t;k)$ for $k \in \mathbb{N}$ and $v, t \in \mathbb{R}$ is introduced.We show that the uniform quantile process $\beta_n(t)$ may be approximated on [0,1] by $n^{-1/2} \mathscr{K}(n,t;k)$, at an optimal uniform almost sure rate of $O(n^{-1/2 + 1/2^{k+1}+o(1)})$ for each $k \in \mathbb{N}$.
		Finkelstein, H. The law of the iterated logarithm for empirical distributions.
		Strassen, V. An invariance principle for the law of the iterated logarithm.Wahrsch.
	projecteuclid.org /getRecord?id=euclid.aop/1019160265 (696 words)

	Functional law of the iterated logarithm (Site not responding. Last check: 2007-10-03)
		Necessary and sufficient condition for the Strassen law of the iterated logarithm in non-uniform topologies (joint with P. Deheuvels), Ann.
		Rate of convergence in the functional law of the iterated logarithm with non-standard normalizing factors (joint with A. Bulinskii).
		On the functional law of the iterated logarithm for partially observed sums of random variables (joint with N. Gorn).
	math.univ-lille1.fr /~lifshits/ML03.HTM (196 words)

	The Law of the Iterated Logarithm for a Triangular Array of Empirical Processes - Arcones (ResearchIndex)
		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.
		22 The law of the iterated logarithm for empirical distribution..
	citeseer.ist.psu.edu /arcones97law.html (620 words)

	Transactions of the American Mathematical Society
		As an application, new laws of the iterated logarithm are established for kernel density estimators.
		Strassen V. An invariance principle for the law of the iterated logarithm.
		A law of the iterated logarithm for kernel density estimators.
	www.ams.org /tran/2001-353-02/S0002-9947-00-02736-7/home.html (457 words)

	Law of the Iterated Logarithm for a Constant-Gain Linear Stochastic Gradient Algorithm
		Law of the Iterated Logarithm for a Constant-Gain Linear Stochastic Gradient Algorithm
		Law of the Iterated Logarithm for a Constant-Gain Linear Stochastic Gradient Algorithm: SIAM Journal on Control and Optimization Vol.
		These limiting properties are expressed in the form of a functional law of the iterated logarithm.
	epubs.siam.org /sam-bin/dbq/article/33100 (184 words)

	ECP Vol 8, Paper 7 (Abstract) (Site not responding. Last check: 2007-10-03)
		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.
		As an application, we obtain a bounded law of the iterated logarithm for the multivariate t-statistic.
		law of the iterated logarithm, sample covariance, central limit theorem, generalized domain of attraction, multivariate t statistic, extreme values, operator normalization, self normalization.
	www.cirm.univ-mrs.fr /EMIS/journals/EJP-ECP/EcpVol8/paper7.abs.html (112 words)

	Electronic Journal of Probability - Vol. 2 (1997) (Site not responding. Last check: 2007-10-03)
		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.
		Härdle, W. A law of the iterated logarithm for nonparametric regression function estimators.
	www.matem.unam.mx /EMIS/journals/EJP-ECP/_ejpecp/viewarticle4cf8.html?id=1221&layout=abstract (439 words)

	banuelos
		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/bibliography.html (743 words)

	Kuelbs: Strassen's law of the iterated logarithm
		Strassen's functional form of the law of the iterated logarithm is formulated for partial sums of random variables with values in a strict inductive limit of Frechet spaces of Hilbert space type.
		STRASSEN, An invariance principle for the law of the iterated logarithm, Z. verw.
		KURTZ, Berry-Essen Estimates in Hilbert Space and an Application to the Law of the Iterated Logarithm, to appear in the Annals of Probability.
	www-mathdoc.ujf-grenoble.fr /numdam-bin/item?id=AIF_1974__24_2_169_0 (194 words)

	vitas
		Some results in analysis related to the law of the iterated logarithm, with BaÃ±uelos, R., Proceedings of the Special Year in Modern Analysis at the University of Illinois, Berkson, E., Peck, N.T. and Uhl, J., Editors, Cambridge University Press, (1989), 47-80.
		The lower bound in the law of the iterated logarithm for harmonic functions, with BaÃ±uelos, R., and Klemes,
		Mean growth of Bloch functions and Makarov's law of the iterated logarithm, with BaÃ±uelos, R., Proc.
	www.math.ksu.edu /~cnmoore/vitas.html (410 words)

	FPM 1995, vol.1, no.3, pp.623-639 (Site not responding. Last check: 2007-10-03)
		The functional law of the iterated logarithm for associated random fields
		The goal of the paper is to provide simply verifiable conditions to guarantee the validity of the functional law of the iterated logarithm for real-valued associated random field
		The functional law of the iterated logarithm is proved in §3 with the help of 6 lemmas.
	www.ii.uj.edu.pl /EMIS/journals/FPM/eng/95/953/95304.htm (232 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)

	Electronic Journal of Probability - Vol. 1 (1996) (Site not responding. Last check: 2007-10-03)
		In particular, when the Markov process in question is a diffusion, we obtain the integral test corresponding to a law of the iterated logarithm due to Knight.
		Erdos, P., On the law of the iterated logarithm.
		Robbins, H. and Siegmund, D., On the law of the iterated logarithm for maxima and minima.
	www.matem.unam.mx /EMIS/journals/EJP-ECP/_ejpecp/viewarticle2b2c.html?id=1203&layout=abstract (386 words)

	Citations: A self-normalized law of the iterated logarithm for random walk in random scenery - Lewis (ResearchIndex)
		T. Lewis, A self--normalized law of the iterated logarithm for random walk in random scenery, J. Theor.
		3 This is called a self normalized law of the iterated logarithm in that the rate of growth of g n as n 1 is described by a random function of the process itself.
		Lewis (1992), A self-normalized law of the iterated logarithm for random walk in random scenery.
	citeseer.ist.psu.edu /context/362467/0 (456 words)

	M. Arcones' publications
		The law of the iterated logarithm for empirical processes under absolute regularity.
		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 (642 words)

	ECP Vol 8 (2003) Paper 7, Bibliography
		Feller, W.(1968) An extension of the law of the iterated logarithm to variables without variance.
		Griffin, P.S. and Kuelbs, J.D. (1989) Self normalized laws of the iterated logarithm.
		Kuelbs, J. and Ledoux M. (1987) Extreme values and the law of the iterated logarithm.
	www.math.helsinki.fi /EMIS/journals/EJP-ECP/EcpVol8/paper7.bibl.html (241 words)

	DC MetaData for: Some problems related to the functional law of the iterated logarithm (Site not responding. Last check: 2007-10-03)
		The law of the iterated logarithm is one of the most important
		is the functional form of this law considered.
		the functional law of the iterated logarithm for the increments of
	www.minet.uni-jena.de /Math-Net/reports/shadows/99-33report.html (217 words)

	Mary Weiss Abstract (Site not responding. Last check: 2007-10-03)
		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)

	The law of the iterated logarithm for the multivariate kernel mode estimator
		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)

	Probability Abstract Service
		We characterize this distribution as the convolution of the law of $D_{i,i+1}$ and $n-i-1$ Bernoulli distributions.
		We further characterize the law of $D_{i,i+1}$ as a mixture of sums of Bernoullis.
		In this paper,we give two theorems giving the law of local-times-process of B at certain stop- ping times, and a description of characteristic measure of the excursions of B from the origin.
	www.math.u-psud.fr /~paserv/Letters/letter_24.html (3113 words)

	Sankhya: The Indian Journal of Statistics (Site not responding. Last check: 2007-10-03)
		An upperclass law of the iterated logarithm for supermartingles is proved, extending a result of Stout.
		The special case of independent random variables satisfying conditions related to the Kolmogorov law of the iterated logarithm is also discussed.
		Law of the iterated logarithm, supermartingales, i.i.d random variables
	sankhya.isical.ac.in /search/48a3/48a3002.htm (56 words)

	A Finitely Additive Version of the Law of the Iterated Logarithm
		A Finitely Additive Version of the Law of the Iterated Logarithm: Theory of Probability & Its Applications Vol.
		A finitely additive version of the law of the iterated logarithm (LIL) is proposed.
		It is also proved that in the case where one deals with $\sigma$-additive probabilities, the given result is equivalent to the classical version of the LIL.
	epubs.siam.org /sam-bin/dbq/article/97788 (134 words)

	Probability Surveys - Vol. 2 (2005)
		Feller, W. (1968) An extension of the law of the iterated logarithm to variables without variance.
		Giné, E. and Mason, D. (2004) The law of the iterated logarithm for the integrated squared deviation of a kernel density estimator.
		Strassen, V. (1966) A converse to the law of the iterated logarithm.
	www.i-journals.org /ps/viewarticle.php?id=50&layout=abstract (541 words)

	The Law of the Iterated Logarithm for p-Random Sequences (Site not responding. Last check: 2007-10-03)
		The Law of the Iterated Logarithm for p-Random Sequences
		It is shown that the law of the iterated logarithm holds for p-random sequences.
		"The Law of the Iterated Logarithm for p-Random Sequences," ccc, p.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/proceedings/&toc=comp/proceedings/ccc/1996/7386/00/7386toc.xml&DOI=10.1109/CCC.1996.507680 (168 words)

	List of publications
		Large deviations and law of the iterated logarithm for partial sums normalized by the largest absolute observation.
		On a new law of iterated logarithm of Erdos and Revesz Acta Math.
		The law of the iterated logarithm for negatively associated random variables.
	darkwing.uoregon.edu /~qmshao/pub/pub.htm (1401 words)

	DC MetaData for:Integral Means and the Law of the Iterated Logarithm
		DC MetaData for:Integral Means and the Law of the Iterated Logarithm
		Integral Means and the Law of the Iterated Logarithm
		univalent functions, the Brennan conjecture, integral means, lacunary series, the law of the iterated logarithm.
	www.ml.kva.se /preprints/meta/KayumovMon_Jun_10_12_08_06.rdf.html (61 words)

	CAT.INIST
		The law of the iterated logarithm for the multivariate nearest neighbor density estimators
		The aim of the present paper is to obtain sharp pointwise rates of strong consistency by establishing a law of the iterated logarithm for this class of estimators.
		We also study the local estimation of a density function based on censored data by the kernel smoothing method using a nearest neighbor approach and derive a law of the iterated logarithm
	cat.inist.fr /?aModele=afficheN&cpsidt=3501817 (317 words)

	Banuelos, Moore: Distribution function inequalities for the density of the area integral
		We also prove a Kesten type law of the iterated logarithm for harmonic functions.
		KLEMES and C.N. An analogue of Kolmogorov's law of the iterated logarithm for harmonic functions, Duke Math.
		BAÑUELOS and C.N. Laws of the iterated logarithm, sharp good-λ inequalities and Lp estimates for caloric and harmonic functions, Indiana Univ. Math.
	www-mathdoc.ujf-grenoble.fr /numdam-bin/item?id=AIF_1991__41_1_137_0 (420 words)

	PKP Open Archives Harvester: View Record (Site not responding. Last check: 2007-10-03)
		compact law of the iterated logarithm for a certain type of
		the iterated logarithm for a class of density estimators.
		60B12, 60F15; Empirical process, law of the iterated logarithm, triangular array, density estimation.
	www.kevinjamieson.com /harvester/viewrecord.php?id=1445 (167 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)

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