Summary
A renewal theorem is obtained for stationary sequences of the form ξn=ξ(...,X n-1,X n,X n+1...), whereX n,\(n \in \mathbb{Z}\), are i.i.d. r.v.s. valued in a Polish space. This class of processes is sufficiently broad to encompass functionals of recurrent Markov chains, functionals of stationary Gaussian processes, and functionals of one-dimensional Gibbs states. The theorem is proved by a new coupling construction.
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Research supported by the National Science Foundation
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Lalley, S.P. Renewal theorem for a class of stationary sequences. Probab. Th. Rel. Fields 72, 195–213 (1986). https://doi.org/10.1007/BF00699103
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DOI: https://doi.org/10.1007/BF00699103