Ergodicity of Spitzer's renewal model
Assume at each point \(x\) of the \(d\)-dimensional integer lattice sits some renewing object with age \(\eta (x)\). It undergoes death and immediate renewal with renewal rate equal to the average age of its closest neighbors plus a constant \(c\). A stochastic process modelling this situation is defined and analysed. It generalizes the process defined by \textit{E. D. Andjel} and \textit{M. E. Vares} [ibid. 42, No. 2, 215-236 (1992; Zbl 0757.60085)] in the case \(d = 1\). The main result states that the process is ergodic if and only if \(c > 0\).
scientific article; zbMATH DE number 735476