A remark on normalizations in a local large deviations principle for inhomogeneous birth-and-death process

A. V. Logachov, Y. M. Suhov, N. D. Vvedenskaya, A. A. Yambartsev

Research output: Contribution to journalArticlepeer-review

Abstract

This work is a continuation of [13].We consider a continuoustime birth – and – death process in which the transition rates are regularly varying function of the process position. We establish rough exponential asymptotic for the probability that a sample path of a normalized process lies in a neighborhood of a given nonnegative continuous function. We propose a variety of normalization schemes for which the large deviation functional preserves its natural integral form.

Original languageEnglish
Pages (from-to)1258-1269
Number of pages12
JournalSiberian Electronic Mathematical Reports
Volume17
DOIs
Publication statusPublished - 2020

Keywords

  • birth – and – death process
  • large deviations principle
  • local large deviations principle
  • normalization (scaling)
  • rate function

OECD FOS+WOS

  • 1.01 MATHEMATICS

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