Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 25, No 1, (1999), 19p-40p
Abstract:
The regenerative excursion process Z(t), t = 0, 1, 2, . . . is
constructed by two independent sequences X = {Xi , i ≥ 1} and Z =
{Ti , (Zi (t), 0 ≤ t < Ti ), i ≥ 1}.
For the embedded alternating renewal process, with interarrival times Xi
– the time for the installation and Ti – the time for the work, are proved
some limit theorems for the spent worktime and the residual worktime, when
at least one of the means of Xi and Ti is infinite.
Limit theorems for the process Z(t) are proved, too.
Finally, some applications to the branching processes with state-dependent
immigration are given.
Description:
This work is supported by Bulgarian NFSI, grant No. MM–704/97
