Darling-Kac theorem for renewal shifts in the absence of regular\n variation

2018/03/28 by Péter Kevei, Kevei, Peter, Dalia Terhesiu +1
Mathematics · #37A50 #60F05 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1803.10700

openalex publication_date 2018/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study null recurrent renewal Markov chains with renewal distribution in\nthe domain of geometric partial attraction of a semistable law. Using the\nclassical procedure of inversion, we derive a limit theorem similar to the\nDarling-Kac law along subsequences and obtain some interesting properties of\nthe limit distribution. Also in this context, we obtain a Karamata type theorem\nalong subsequences for positive operators. In both results, we identify the\nallowed class of subsequences. We provide several examples of nontrivial\ninfinite measure preserving systems to which these results apply.\n

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