E. V. Efremov, A. V. Logachov, “On the moderate deviation principle for <nobr>$m$</nobr>-dependent random variables with sublinear expectation”, Sib. Èlektron. Mat. Izv., 2023, Volume 20, Issue 2,Pages <nobr>961

Probability theory and mathematical statistics

On the moderate deviation principle for $m$-dependent random variables with sublinear expectation

E. V. Efremov^a, A. V. Logachov^bc

^a Novosibirsk State University, 2, Pirogova str., Novosibirsk, 630090, Russia
^b Lab. of Probability Theory and Math. Statistics, Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
^c Dep. of Computer Science in Economics, Novosibirsk State Technical University pr. K. Marksa, 20, 630073, Novosibirsk, Russia

Abstract: In this paper, we obtain the moderate deviation principle for sums of $m$–dependent strictly stationary random variables in the space with sublinear expectation. Unlike known results, we will require random variables to satisfy a less restrictive Cramer-like condition.

Keywords: large deviation principle, moderate deviation principle, sublinear expectation, $m$-dependent random variables, stationary sequences.

UDC: 519.21

MSC: 60F10, 60A99

Received December 31, 2023, published November 12, 2023

Language: English

DOI: 10.33048/semi.2023.20.058