Infinite limits and infinite limit points of random walks and trimmed sums

DOI10.1214/aop/1176988609zbMath0816.60067OpenAlexW2071200458MaRDI QIDQ1345606

Harry Kesten, Ross A. Maller

Publication date: 6 July 1995

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176988609

zbMATH Keywords

divergence along a subsequencegeneralized iterated logarithm law

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Order statistics; empirical distribution functions (62G30) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15)

Related Items (15)

Stochastic bounds for Lévy processes. ⋮ The Joint Distribution of the Sum and the Maximum of IID Exponential Random Variables ⋮ Some effects of trimming on the law of the iterated logarithm ⋮ The joint distribution of the sum and maximum of dependent Pareto risks ⋮ On the limiting behaviour of Lévy processes at zero ⋮ On the ladder heights of random walks attracted to stable laws of exponent 1 ⋮ Limit theorems for mixed max-sum processes with renewal stopping ⋮ A note on summability of ladder heights and the distributions of ladder epochs for random walks ⋮ Distributional representations and dominance of a Lévy process over its maximal jump processes ⋮ A LIL and limit distributions for trimmed sums of random vectors attracted to operator semi-stable laws ⋮ Overshoots over curved boundaries ⋮ Renewal theorems and stability for the reflected process ⋮ Weak laws of large numbers for cooperative gamblers ⋮ A renewal theorem for relatively stable variables ⋮ Weak Convergence of Self-normalized Partial Sums Processes

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