Summary
We develop several strong approximations for k-th records and k-th record times by Wiener processes. Our main result is that it is possible to approximate by the same Wiener process up to the almost sure rate O(log j), where j stands for the index of the observations, the k-th records, the logarithms of the k-th record times, and the logarithms of the k-th interrecord times. We also provide some limiting weak laws and obtain Berry-Esséen-type theorems for k-th record times.
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Deheuvels, P. Strong approximations of k-th records and k-th record times by Wiener processes. Probab. Th. Rel. Fields 77, 195–209 (1988). https://doi.org/10.1007/BF00334037
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DOI: https://doi.org/10.1007/BF00334037
Keywords
- Stochastic Process
- Probability Theory
- Statistical Theory
- Wiener Process
- Record Time