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

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

Journal

Stochastic Processes and their Applications
ISSN: 0304-4149

Output data

Year: 2021, Volume: 137, Pages: 149-166 Pages count : 18 DOI: 10.1016/j.spa.2021.03.011

Tags

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

Authors

Logachov A. ^1,2 , Mogulskii A. ^1,2 , Prokopenko E. ^1,2,3 , Yambartsev A. ⁴

Affiliations

1	Sobolev Institute of Mathematics of SB RAS, Novosibirsk, Russian Federation
2	Novosibirsk State University, Novosibirsk, Russian Federation
3	ESSEC Business School, Paris, France
4	Institute of Mathematics and Statistics, University of São Paulo (USP), São Paulo, SP, 05508-090, Brazil

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. © 2021 Elsevier B.V.

Logachov A. , Mogulskii A. , Prokopenko E. , Yambartsev A.
Local theorems for (multidimensional) additive functionals of semi-Markov chains
Stochastic Processes and their Applications. 2021. V.137. P.149-166. DOI: 10.1016/j.spa.2021.03.011 WOS Scopus OpenAlex

Web of science:	WOS:000654207400005
Scopus:	2-s2.0-85104050159
OpenAlex:	W3141721417

DB	Citing
Scopus	2
OpenAlex	3
Web of science	2