Title: A New Duality Relation for Random Walks
Authors: Holger Dette and Jim Pitman and William Studden
Date: July 1995
Abstract:
For the random walk on the nonnegative integers with reflecting barrier it
is shown that the right tails of the probability of the first return from
state $0$ to state $0$ are simple transition probabilities of a
``dual''random walk which is obtained from the original process by
interchanging the one step probabilities. A combinatorical and analytical
proof are presented and extensions and relations to other concepts of
duality in the literature are discussed.