N. D. Vvedenskaya, A. V. Logachov, Yu. M. Suhov, A. A. Yambartsev, “A local large deviation principle for inhomogeneous birth-death processes”, Probl. Peredachi Inf., 2018, Volume 54, Issue 3,Pages <nobr>73

This article is cited in 5 papers

Large Systems

A local large deviation principle for inhomogeneous birth-death processes

N. D. Vvedenskaya^a, A. V. Logachov^bcd, Yu. M. Suhov^ea, A. A. Yambartsev^f

^a Dobrushin Mathematical Laboratory, Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
^b Laboratory of Applied Mathematics, Novosibirsk State University, Novosibirsk, Russia
^c Statistics Division, Novosibirsk State University of Economics and Management, Novosibirsk, Russia
^d Laboratory of Probability Theory and Mathematical Statistics, Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
^e Mathematical Department, Pennsylvania State University, University Park, State College, USA
^f Department of Statistics, Institute of Mathematics and StatisticsUniversity of São Paulo, São Paulo, Brazil

Abstract: The paper considers a continuous-time birth-death process where the jump rate has an asymptotically polynomial dependence on the process position. We obtain a rough exponential asymptotic for the probability of trajectories of a re-scaled process contained within a neighborhood of a given continuous nonnegative function.

UDC: 621.391.1:519.2

Received: 17.11.2016
Revised: 12.02.2018