On the Law of the Iterated Logarithm

From MaRDI portal
Publication:5778367

DOI10.2307/2371287zbMath0024.15802OpenAlexW2314546542WikidataQ94784915 ScholiaQ94784915MaRDI QIDQ5778367

Philip Hartman, Aurel Wintner

Publication date: 1941

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2371287



Related Items

A law of the iterated logarithm for processes with independent increments, Kolmogorov type law of the logarithm for arrays, Some mean convergence theorems for arrays of rowwise pairwise negative quadrant dependent random variables, Contributions to the Theory of Markov Chains. II, Some Strong Laws of Large Numbers for Banach Space Valued Summands Irrespective of Their Joint Distributions, ON THE STRONG LAW OF LARGE NUMBERS FOR SUMS OF INDEPENDENT BANACH SPACE VALUED RANDOM ELEMENTS, A NONCLASSICAL LAW OF THE ITERATED LOGARITHM FOR I.I.D. SQUARE INTEGRABLE RANDOM VARIABLES. II, The General Form of the So-Called Law of the Iterated Logarithm, On the rate of convergence in the strong law of large numbers for arrays, Some effects of trimming on the law of the iterated logarithm, PROPERTIES OF PREDICTORS FOR MULTIVARIATE AUTOREGRESSIVE MODELS WITH ESTIMATED PARAMETERS, Between the LIL and the LSL, A universal form of the Chung-type law of the iterated logarithm, Invariance principles for the law of the iterated logarithm under \(G\)-framework, On the value distribution of the Epstein zeta function in the critical strip, The law of the iterated logarithm for spatial averages of the stochastic heat equation, An exact asymptotic for the square variation of partial sum processes, A Note Concerning Behaviour of Iterated Logarithm Type, Almost sure limit behaviour of Cesàro sums with small order, COMPLETE CONVERGENCE FOR ARRAYS AND THE LAW OF THE SINGLE LOGARITHM, Unnamed Item, A Supplement to the Einmahl–Li Results on Two-Sided Iterated Logarithm Type Behavior for I.I.D. Random Variables, On moments of the supremum of normed weighted averages, Laws of iterated logarithm for state variables with applications, The limit law of the iterated logarithm, On the path properties of a lacunary power series, Kolmogorov's law of the iterated logarithm for noncommutative martingales, Law of the iterated logarithm for stationary processes, A NONCLASSICAL LAW OF THE ITERATED LOGARITHM FOR I.I.D. SQUARE INTEGRABLE RANDOM VARIABLES, Laws of the iterated logarithm for sample moments and applications, A nonclassical law of the iterated logarithm for self-normalized partial sums, The law of the iterated logarithm on subsequences-characterizations, Convergence rates for probabilities of moderate deviations for multidimensionally indexed random variables, A REMARK ON THE STRONG LAW FOR B-VALUED ARRAYS OF RANDOM ELEMENTS, Strassen type limit points for moving averages of a wiener process, Laws of the single logarithm for delayed sums of random fields, On a flexible class of continuous functions with uniform local structure, Complete convergence of bootstrapped means and moments of the supremum of normed bootstrapped sums, Convergence Rate for a Large Deviation Probability, A glimpse of the impact of pál erdős on probability and statistics, Asymptotic properties for the moment estimators in Rayleigh distribution with two parameters, Strong laws of large numbers for the sequence of the maximum of partial sums of i.i.d. random variables, The law of the iterated logarithm for a piecewise deterministic Markov process assured by the properties of the Markov chain given by its post-jump locations, On the Set of Limit Points of Normed Sums of Geometrically Weighted I.I.D. Bounded Random Variables, A Law of the Iterated Logarithm for Stable Summands, The Davis-Gut law and Lai law for finitely inhomogeneous walks, On the critical case of Okamoto's continuous non-differentiable functions, Some results on two-sided LIL behavior, Generalized Law of the Iterated Logarithm and Its Convergence Rate, Some One-Sided Theorems on the Tail Distribution of Sample Sums with Applications to the Last Time and Largest Excess of Boundary Crossings, Strong law for linear processes, On the law of the iterated logarithm for arrays of random variables, Fluctuation Theory of Recurrent Events, The effect of splitting on random forests, Invariance principles for sums of Banach space valued random elements and empirical processes, The Law of the Iterated Logarithm for Brownian Motion in a Banach Space, A subsequence principle in probability theory (applied to the law of the iterated logarithm), A converse to the log-log law for Martingales, On rates of convergence for sample average approximations in the almost sure sense and in mean