Confidence Interval. In the context of Example 66, suppose the regenerative-increment process Z(t) is not observed continuously over time, but only observed at its regeneration times Tn. In this case,...

Confidence Interval. In the context of Example 66, suppose the regenerative-increment process Z(t) is not observed continuously over time, but only observed at its regeneration times Tn. In this case, the information observed up to the nth regeneration time T_n
is {Z(t) : t ≤ T_n}. First, find the a.s. limit of Z(T_n)/n, and the limiting distribution of (Z(T_n) − aTn)/n^1/2Example 66