Resumen de Central Limit theorems for records

Raúl Gouet Bañares , Francisco Javier López Lorente , Gerardo Sanz Sáiz

• nsider a sequence (Xn) of independent and identically distributed random variables, taking nonnegative integer values and call Xn a record if Xn > max{X1, . . . , Xn-1}. In Gouet et al. (2001), a martingale approach combined with asymptotic results for sums of partial minima was used to derive strong convergence results for the number of records among the first n observations. Now, in this paper we exploit the connection between records and martingales to establish a central limit theorem for the number of records in many discrete distributions, identifying the centering and scaling sequences.