On a joint strong approximation theorem for record and inter-record times |
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| Authors: | D Pfeifer |
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| Institution: | (1) Institut für Statistik und Wirtschaftsmathematik, Technische Universität Aachen, Wüllnerstrasse 3, D-5100 Aachen, Germany;(2) University of North Carolina at Chapel Hill, Chapel Hill, USA |
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| Abstract: | Summary We present a simple joint strong approximation for the logarithms of record and inter-record times from an exchangeable sequence, including an exact estimation for the rate of convergence in terms of upper and lower class functions of a Wiener process. The approach chosen here allows for simple proofs of exact and asymptotic (joint) results for record and inter-record times, such as the Law of Large Numbers (LLN), Central Limit Theorem (CLT) and Law of the Iterated Logarithm (LIL), and others.Research supported by the Air Force Office of Scientific Research Contract No. F49620 85 C0144 |
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