Past exam of the mathematics course of the University of Cambridge / 2010 / ii / Paper 4 / 26I / a / iii / Solution

A recurrent state is positive recurrent if its expected elapsed return-cycle time is finite. The cycle starts on entering the state and ends at its next entrance after a departure; it includes the initial holding time. This convention avoids counting the immediate return caused by a right-continuous path remaining at its initial state.