Partial Sum Process for Records

摘要

Suppose the upper records {X_(Ln)} from a sequence of i.i.d. random variables is in the domain of attraction of a normal distribution. Consider the D(0,1]-valued process {Z_n(·)} constructed by usual interpolation of the partial sums of the records. We prove that under some mild conditions, {Z_n} converges to a limiting Gaussian process in D(0,l]. As a consequence, the partial sums of records is asymptotically normal.