| Records from the sequence Y(,n) = X(,n) + cn, n (GREATERTHEQ) 1, are analyzed, where X(,n) is a strictly stationary random sequence. We prove the almost sure convergence of the record rate, record times, and record values to specified constants. Under appropriate moment assumptions and mixing conditions, central limit theorems are also shown to hold for the above-mentioned sequences. Moreover, a more stringent moment condition leads to a law of the iterated logarithm for the record rate. The special case when X(,n) is a stationary Gaussian process is considered with special attention given to Gaussian ARMA sequences.;The weak convergence of sample extremes for Y(,n) is briefly considered, leading to a characterization of the type II extreme value distribution. Finally, in the special case when X(,n) is i.i.d. with.;type I extreme value distribution, we may embed the sequence of successive maxima.;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;A class of weakly consistent estimators for the asymptotic variance of the record rate is constructed. The performance of several of these estimators for small samples is examined via a simulation study. All these results are illustrated by analysis of the times in the 400 and 800 meter runs.;in a suitable extremal process. This leads to several independence results for certain random sequences which are functions of the sample maxima. Also, in this situation, we prove that the inter- record times are asymptotically geometric. |
