On distributionally regenerative processes (Q1337945)

Regenerative processes have played a major role in the theory and applications of stochastic processes. Less well-known are the distributionally regenerative processes, also called equilibrium processes, where the standard regeneration condition is replaced by a weakened version. In the main result it is shown that distributional regeneration is equivalent to renewal representation of the associated shift operator. Sufficient conditions for distributional regeneration are given for a number of Markov chain applications.