Large Systems

Large deviation principle for terminating multidimensional compound renewal processes with application to polymer pinning models

A. V. Logachov^abc, A. A. Mogulskii^ac, E. I. Prokopenko<sup>ca

a</sup> Novosibirsk State University, Novosibirsk, Russia
^b Novosibirsk State Technical University, Novosibirsk, Russia
^c Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: We obtain a large deviations principle for terminating multidimensional compound renewal processes. We also obtain the asymptotics of large deviations for the case where a Gibbs change of the original probability measure takes place. The random processes mentioned in the paper are widely used in polymer pinning models.

Keywords: compound renewal process, large deviations principle, rate function, polymer pinning models, Gibbs change of the probability measure.

UDC: 621.391 : 519.214 : 519.218.4

Received: 23.12.2021
Revised: 28.03.2022
Accepted: 30.03.2022

DOI: 10.31857/S0555292322020053

 English version: Problems of Information Transmission, 2022, 58:2, 144–159