1 results
Hitting times of decreasing sets for regenerative processes
-
- Journal:
- Journal of Applied Probability / Volume 25 / Issue 1 / March 1988
- Published online by Cambridge University Press:
- 14 July 2016, pp. 89-96
- Print publication:
- March 1988
-
- Article
- Export citation
-
Let {X(t): t ≧ 0} be a regenerative process with excursion process {Y(u): 0 ≦ u < T, T} and state space
. Let An be a sequence of sets in 
such that pn=P(Y(u)∊An for some 0≦ u < T) → 0. Let Vn be the hitting time of An for the process X. This paper gives a variety of conditions on the excursion process Y to obtain limit theorems for Vn. Apart from obtaining an exponential limit in the positive recurrent case, i.e. ET < x, some non-exponential limits are obtained in the null recurrent case. The results are illustrated via the age process.
. Let 
such that 