Approximate formulas for stationary characteristics of a renewal-reward process in a strip

Xanıyev T., Hanalioglu Z., Poladova A.

Demonstratio Mathematica, vol.59, no.1, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 59 Issue: 1
  • Publication Date: 2026
  • Doi Number: 10.1515/dema-2025-0230
  • Journal Name: Demonstratio Mathematica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Linguistic Bibliography, MathSciNet, zbMATH, Directory of Open Access Journals
  • Keywords: approximated formulas, ergodic distribution, Error function, renewal-reward process in a strip, weak convergence
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

This study examines a modification of a renewal-reward process in a strip. First, the study proves that this process is ergodic under certain conditions. Then, the exact formulas are obtained for the ergodic distribution and moments of the process in the subject. Moreover, using the asymptotic properties of the Error function and the Laplace transform, we derive two-term asymptotic expansions for the ergodic distribution and its moments. Finally, using these expansions, the study proves that the ergodic distribution of the standardized process weakly converges to a uniform distribution.