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- Title
Open problems in renewal, coupling and Palm theory.
- Authors
Thorisson, Hermann
- 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.
- Subjects
RENEWAL theory; RANDOM walks; LIMIT theorems; DISTRIBUTION (Probability theory); MEASURE theory
- Publication
Queueing Systems, 2011, Vol 68, Issue 3/4, p313
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-011-9241-2