Please use this identifier to cite or link to this item: http://hdl.handle.net/1946/5480
The main focus of this thesis is on coupling of random walks on the line with discrete step lengths and initial positions. After introducing the relevant coupling concepts, an Ornstein-type approach is used to establish necessary and sufficient conditions for the existence of a successful
exact coupling and a successful shift-coupling. This yields results on asymptotic loss of memory. These findings are then applied to establish successful exact coupling of continuous-time regenerative processes with discrete regeneration times. After preliminaries on extension techniques, we finally construct a successful exact coupling of random walks with non-discrete (possibly singular) step lengths that are periodic in a certain sense.