Open problems in renewal, coupling and Palm theory

Hermann Thorisson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

This note presents four sets of problems. The first suggests the possibility of a limit theory for null-recurrent renewal processes similar to the theory in the positive recurrent case. The second concerns exact coupling of random walks on the line with step-lengths that are neither discrete nor spread out. The third concerns the coupling characterization of setwise convergence of distributions of stochastic processes to a stationary limit. The fourth concerns characterizations of mass-stationarity, a concept formalizing the intuitive idea that the origin is a typical location in the mass of a random measure. Mass-stationarity is an intrinsic characterization of Palm versions with respect to stationary random measures.

Original languageEnglish
Pages (from-to)313-319
Number of pages7
JournalQueueing Systems
Volume68
Issue number3
DOIs
Publication statusPublished - Aug 2011

Other keywords

  • Coupling
  • Palm theory
  • Random walk
  • Renewal process

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