On the tail behavior of sums of independent random variables

DOI10.1007/BF00535464zbMath0339.60050MaRDI QIDQ4107712

Leo Breiman

Publication date: 1967

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50)

Related Items (19)

Potential Processes ⋮ On the other law of the iterated logarithm ⋮ On the other LIL for variables without finite variance ⋮ On the deviations in the Skorokhod-Strassen approximation scheme ⋮ Rates of convergence for increments of Brownian motion ⋮ A remark on the skorohod representation ⋮ Dynamical attraction to stable processes ⋮ Maxima of partial sums of independent random variables ⋮ A Strong Law of Large Numbers for Martingales ⋮ Skorohod embedding of multivariate RV's, and the sample DF ⋮ Strong approximation of partial sums under dependence conditions with application to dynamical systems ⋮ Rate of strong Gaussian approximation for sums of i.i.d. multidimensional random vectors ⋮ Strong approximation for set-indexed partial sum processes via KMT constructions III ⋮ On the lower limits of maxima and minima of wiener process and partial sums ⋮ On the invariance principle for sums of independent identically distributed random variables ⋮ Simple random walk on the line in random environment ⋮ The accuracy of strong Gaussian approximation for sums of independent random vectors ⋮ Strong invariance for local times ⋮ A new method to prove strassen type laws of invariance principle. 1

Cites Work

• Unnamed Item
• An invariance principle for the law of the iterated logarithm
• On rates of convergence for the invariance principle
• On the Maximum Partial Sums of Sequences of Independent Random Variables
• A Limit Theoerm for Random Variables with Infinite Moments

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