2019/05/27 by Nickos Papadatos, Papadatos, Nickos
Mathematics · Physics and Astronomy · #44A60 (Secondary) #60E05 #62G30 (Primary) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1905.11464
openalex publication_date 2019/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate conditions in order to decide whether a given sequence of real numbers represents expected record values arising from an independent, identically distributed, sequence of random variables. The main result provides a necessary and sufficient condition, relating any expected record sequence with the Stieltjes moment problem. The results are proved by means of a useful transformation on random variables. Some properties of this mapping, and its inverse, are discussed in detail, and, under mild conditions, an explicit inversion formula for the random variable that admits a given expected record sequence is obtained. Key words and phrases: characterizations; expected record values; Stieltjes moment problem; transformation of random variables; inversion formula. AMS subject classification: Primary 60E05, 62G30; Secondary 44A60.