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

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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.

Original languageEnglish
Pages (from-to)149-166
Number of pages18
JournalStochastic Processes and their Applications
Volume137
DOIs
Publication statusPublished - Jul 2021

Keywords

  • Continuous-time random walk
  • Large deviations
  • Local limit theorem
  • Renewal process
  • Semi-Markov chain

OECD FOS+WOS

  • 1.01 MATHEMATICS

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