Independent poisson processes generated by record values and inter-record times

AbstractThe mth-order upper record values of a sequence of independent random variables with common continuous distribution function, that are kth but not (k-1)th-order record values and that precede inter-record times of length j, form a Poisson process, the processes for different (k,j) being independent, k = 1,..., m, j = 1,2,.... The records with record epochs after r\2>m, have a similar property if we condition with respect to the mth decreasing order statistic of the sample for times 1,..., r. These results extend theorems by Ignatov