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Local theorems for (multidimensional) additive functionals of semi-Markov chains. / Logachov, Artem; Mogulskii, Anatolii; Prokopenko, Evgeny et al.

In: Stochastic Processes and their Applications, Vol. 137, 07.2021, p. 149-166.

Research output: Contribution to journal › Article › peer-review

Harvard

Logachov, A, Mogulskii, A, Prokopenko, E & Yambartsev, A 2021, 'Local theorems for (multidimensional) additive functionals of semi-Markov chains', Stochastic Processes and their Applications, vol. 137, pp. 149-166. https://doi.org/10.1016/j.spa.2021.03.011

APA

Logachov, A., Mogulskii, A., Prokopenko, E., & Yambartsev, A. (2021). Local theorems for (multidimensional) additive functionals of semi-Markov chains. Stochastic Processes and their Applications, 137, 149-166. https://doi.org/10.1016/j.spa.2021.03.011

Vancouver

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

Author

Logachov, Artem ; Mogulskii, Anatolii ; Prokopenko, Evgeny et al. / Local theorems for (multidimensional) additive functionals of semi-Markov chains. In: Stochastic Processes and their Applications. 2021 ; Vol. 137. pp. 149-166.

BibTeX

@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.",

}

RIS

TY - JOUR

T1 - Local theorems for (multidimensional) additive functionals of semi-Markov chains

AU - Logachov, Artem

AU - Mogulskii, Anatolii

AU - Prokopenko, Evgeny

AU - Yambartsev, Anatoly

N1 - 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’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: © 2021 Elsevier B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/7

Y1 - 2021/7

N2 - 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.

AB - 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.

KW - Continuous-time random walk

KW - Large deviations

KW - Local limit theorem

KW - Renewal process

KW - Semi-Markov chain

UR - http://www.scopus.com/inward/record.url?scp=85104050159&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2021.03.011

DO - 10.1016/j.spa.2021.03.011

M3 - Article

AN - SCOPUS:85104050159

VL - 137

SP - 149

EP - 166

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

ER -

ID: 28364968