Limit Theory for Taboo-Regenerative Processes
P. W. Glynn and H. Thorisson
Queueing Systems: Theory and Applications, 271-294 (2004)
The paper considers the two-sided taboo limit process that arises when a regenerative process X is conditioned on staying out of a specified set of states (taboo set) over a long period of time. The taboo limit process after time 0 is a version of X, and the time-reversal of the taboo limit process before time 0 is regenerative with tabooed cycles having exponentially biased lengths. The cycle straddling zero has that same bias up to time 0, and is unbiased after time 0. This extends to processes regenerative in the wide sense, and to processes that only regenerate as long as they have not entered the taboo set.