A Coupling, and the Darling-Erdos Conjectures

2005/11/17 by Davar Khoshnevisan, David Levin, Khoshnevisan, Davar +2
Economics, Econometrics and Finance · Mathematics · #60F15 #60G70 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60F15 #msc:60G70

paper · pdf · doi:10.48550/arxiv.math/0511429

13 pages

arxiv created 2005/11/17 · openalex publication_date 2005/11/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive a new coupling of the running maximum of an Ornstein-Uhlenbeck process and the running maximum of an explicit i.i.d. sequence. We use this coupling to verify a conjecture of Darling and Erdos (1956).

Citations

• Some Limit Theorems for Random Functions. II
• Almost sure invariance principles for partial sums of weakly dependent random variables
• On the Law of the Iterated Logarithm

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