On a Joint Strong Approximation Theorem for Record and Inter-Record Times.
NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS
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This report presents 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, Central Limit Theorem and Law of the Interated Logarithm, and others. Keywords Markov chains Stochastic processes Random variables. Author
- Statistics and Probability