The Markov Oscillation Problem in Discrete Time
Yonglong Dai, Eric Renshaw · Journal of the London Mathematical Society · 2000
Consider a discrete-time regenerative phenomenon with associated renewal sequence un. General results for the supremum of um+1, …, um+n are developed for those renewal sequences {un} for which the first m + 1 elements match those of a fixed renewal sequence {vn}, that is, u0 = v0, …, um = vm. A series of associated lemmas are developed in the process.