Renewal theorems for processes with dependent interarrival times

Sabrina Kombrink*

*Corresponding author for this work


In this paper we develop renewal theorems for point processes with interarrival times ξ(Xn+1Xn... ), where (Xn)nâ is a stochastic process with finite state space Σ and ξ:ΣA→â" is a Hoälder continuous function on a subset ΣAâc'Σâ". The theorems developed here unify and generalise the key renewal theorem for discrete measures and Lalley's renewal theorem for counting measures in symbolic dynamics. Moreover, they capture aspects of Markov renewal theory. The new renewal theorems allow for direct applications to problems in fractal and hyperbolic geometry, for instance to the problem of Minkowski measurability of self-conformal sets.

Original languageEnglish
JournalAdvances in Applied Probability
Issue number4
Pages (from-to)1193-1216
Number of pages24
Publication statusPublished - 01.12.2018


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