A NOTE ON THE EXISTENCE OF REGENERATION TIMES

We rigorously prove that for a stochastic process, X = {X(t) : t great er than or equal to 0}, the existence of a first regeneration time, R( 1), implies the existence of an infinite sequence of such times, {R(1) , R(2),...}, and hence that the definition of regenerative process nee d only demand the existence of a first regeneration time. Here we incl ude very general processes up to and including processes where cycles are stationary but not necessarily independent and identically distrib uted.