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.
References
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Research supported by the Air Force Office of Scientific Research Contract No. F49620 85 C0144
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Pfeifer, D. On a joint strong approximation theorem for record and inter-record times. Probab. Th. Rel. Fields 75, 213–221 (1987). https://doi.org/10.1007/BF00354034
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DOI: https://doi.org/10.1007/BF00354034
Keywords
- Stochastic Process
- Probability Theory
- Limit Theorem
- Statistical Theory
- Central Limit