Open problems in renewal, coupling and Palm theory

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.