@article{17afad58b8b94f3ca21dd11e9bbd4628,
title = "Local theorems for (multidimensional) additive functionals of semi-Markov chains",
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, Large deviations, Local limit theorem, Renewal process, Semi-Markov chain",
author = "Artem Logachov and Anatolii Mogulskii and Evgeny Prokopenko and Anatoly Yambartsev",
note = "Funding Information: This work was supported by RSF, Russia project 18-11-00129 . This work was partly funded by CY Initiative of Excellence, France (grant “Investissements d{\textquoteright}Avenir” ANR-16-IDEX-0008 ); Evgeny Prokopenko acknowledges with gratitude the hospitality of ESSEC CREAR. Anatoly Yambartsev thanks FAPESP, Brazil grant 2017/10555-0 . Publisher Copyright: {\textcopyright} 2021 Elsevier B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = jul,
doi = "10.1016/j.spa.2021.03.011",
language = "English",
volume = "137",
pages = "149--166",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier Science Publishing Company, Inc.",
}