Local theorems for (multidimensional) additive functionals of semi-Markov chains

Artem Logachov, Anatolii Mogulskii, Evgeny Prokopenko and Anatoly Yambartsev

Stochastic Processes and their Applications, 2021, vol. 137, issue C, 149-166

Abstract: We consider a (multidimensional) additive functional of semi-Markov chain, defined by an ergodic Markov chain with a finite number of states. The distribution of random vectors, governing the process, is supposed to be lattice and light-tailed. We derive the exact asymptotics in the local limit theorem. As a consequence, we establish a local central limit theorem.

Keywords: Continuous-time random walk; Renewal process; Semi-Markov chain; Local limit theorem; Large deviations (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spa.2021.03.011

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