This note is concerned with the identification of the Wiener-Hopf factors of a function $1-f$, where $f$ generates an aperiodic distribution on the integers with a negative mean. The general and rational cases are addressed. We give a concise summary of the main practical facts needed for calculations involving the Wiener-Hopf factors. The basic facts are cited from the literature, but a few aspects are briefly proven here.

Characteristic functions; other transforms (msc 60E10), Markov chains (discrete-time Markov processes on discrete state spaces) (msc 60J10), Markov processes (msc 60Jxx)
CWI
Department of Operations Research, Statistics, and System Theory [BS]

Bayer, N. (1995). On the identification of Wiener-Hopf factors. Department of Operations Research, Statistics, and System Theory [BS]. CWI.