TY - JOUR

T1 - Excursions of Markov Processes: A Large Deviation Approach

AU - Logachov, A.

AU - Mogulskii, A.

AU - Suhov, Y.

AU - Yambartsev, A.

N1 - A. Logachov is supported by FAPESP grant 2022/01289-3 for financial support and by the Ministry of Science and Higher Education of the Russian Federation grant FWNF-2022-0010. †A. Mogulskii is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2022-282 with the Ministry of Science and Higher Education of the Russian Federation. ‡A. Yambartsev is supported by FAPESP grant 2022/01289-3 for financial support and FAPESP grant 2017/10555-0 for financial support. Публикация для корректировки.

PY - 2023

Y1 - 2023

N2 - This paper is dedicated to the memory of Nikita Dmitrievna Vve-denskaya. 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.

AB - This paper is dedicated to the memory of Nikita Dmitrievna Vve-denskaya. 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.

KW - Markov process

KW - birth and death process

KW - large deviations principle

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85171970550&origin=inward&txGid=fd8457259ba4c1b5d03d3f8594316135

UR - https://www.mendeley.com/catalogue/c77ea1d7-dfd5-3545-ab02-d18bf07523d3/

M3 - Article

VL - 29

SP - 189

EP - 197

JO - Markov Processes And Related Fields

JF - Markov Processes And Related Fields

SN - 1024-2953

IS - 2

ER -