Extremal Processes, Record Times and Strong Approximation.
NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES
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Given an i.i.d. sequence of random variables r.v.s with continuous cumulative distribution function CDF F, the author presents a simple construction for the jump times of an extremal process on the same probability space which interpolate the given record times. This gives another approach to the strong approximation of extremal processes as developed by Deheuvels 1981, 1982, 1983, and allows for a more detailed investigation of the relationship between the record times of the given sequence and the jump times of the extremal process. In particular, it is shown that the number S of surplus jump time points in 1, infinity over the record times is approximately Poisson distributed with an exact mean of ES 1 - C, C denoting Eulers constant. Keywords Poisson approximation. Author
- Statistics and Probability