Excursions of Markov Processes: A Large Deviation Approach

Excursions of Markov Processes: A Large Deviation Approach Full article

Journal

Markov Processes and Related Fields
ISSN: 1024-2953

Output data

Year: 2023, Volume: 29, Number: 2, Pages: 189-197 Pages count : 9

Tags

Markov process, birth and death process, large deviations principle

Authors

Logachov A. ^1,2 , Mogulskii A. ^1,3 , Suhov Y. ^4,5 , Yambartsev A. ⁶

Affiliations

1	Sobolev Institute of Mathematics of Siberian Branch of Russian Academy of Sciences
2	Novosibirsk State Technical University
3	Novosibirsk State University
4	Penn State University
5	University of Cambridge
6	Department of Statistics, Institute of Mathematics and Statistics, University of Sao Paulo

Funding (2)

1	Sobolev Institute of Mathematics	FWNF-2022-0010
2	Mathematical Center in Akademgorodok	075-15-2019-1675

This paper is dedicated to the memory of Nikita Dmitrievna Vvedenskaya. These authors had a privilege to collaborate with Vvedenskaya during the last period of her life. The paper considers a buyer-seller interaction model based on a two-dimensional process. The first coordinate is the number of buyers and the second one is the number of sellers. The rates of the income and outcome of sellers and buyers depend on their numbers polynomially at a given time. To make the process ergodic we require that the intensity of outcome has a higher degree. The problem associated with positive excursions of the trajectories of such processes is being solved. A local principle of large deviations for these excursions is obtained.

Logachov A. , Mogulskii A. , Suhov Y. , Yambartsev A.
Excursions of Markov Processes: A Large Deviation Approach
Markov Processes and Related Fields. 2023. V.29. N2. P.189-197. WOS Scopus

Submitted:	Sep 28, 2022
Accepted:	May 23, 2023
Published print:	Sep 15, 2023
Published online:	Sep 15, 2023

Web of science:	WOS:001104862100005
Scopus:	2-s2.0-85171970550

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