Strong renewal theorem and local limit theorem in the absence of regular\n variation

2020/05/22 by Péter Kevei, Kevei, Peter, Dalia Terhesiu +1
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2005.11121

Abstract

We obtain a strong renewal theorem with infinite mean beyond regular\nvariation, when the underlying distribution belongs to the domain of geometric\npartial attraction a semistable law with index \α\∈ (1/2,1]. In the\nprocess we obtain local limit theorems for both finite and infinite mean, that\nis for the whole range \α\∈ (0,2). We also derive the asymptotics of the\nrenewal function for \α\∈ (0,1].\n

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