Abstract
Suppose the upper records \({\left\{ {X_{{L_{n} }} } \right\}}\) 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(0,1]. As a consequence, the partial sums of records is asymptotically normal.
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AMS 2000 Subject Classification
Primary—60F17
Secondary—60G70
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Bose, A., Gangopadhyay, S. & Sarkar, A. Partial Sum Process for Records. Extremes 8, 43–56 (2005). https://doi.org/10.1007/s10687-005-4859-2
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DOI: https://doi.org/10.1007/s10687-005-4859-2