PROBABILITY DISTRIBUTIONS RELATED TO THE LAW OF THE ITERATED LOGARITHM

Let W(t) denote a standard Wiener process for 0 ≤ t < ∞. We compute the probability that W(t) ≥ t(½) A(t) for some t ≥ 1 (or for some t ≥ 0) for a certain class of functions A(t), including functions which are ∼ (2 log log t)(½) as t → ∞. We also give an invariance principle which states that this p...

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Опубликовано в::	Proc Natl Acad Sci U S A
Главные авторы:	Robbins, H., Siegmund, D.
Формат:	Artigo
Язык:	Inglês
Опубликовано:	National Academy of Sciences 1969
Предметы:	Physical Sciences: Mathematics
Online-ссылка:	https://ncbi.nlm.nih.govhttps://pmc.ncbi.nlm.nih.gov/articles/PMC285947/ https://ncbi.nlm.nih.govhttps://pubmed.ncbi.nlm.nih.gov/16591726/ https://ncbi.nlm.nih.govhttps://doi.org/10.1073/pnas.62.1.11
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