Limit Theorems for Regenerative Excursion Processes

Mitov, Kosto. "Limit Theorems for Regenerative Excursion Processes." Serdica Mathematical Journal 25.1 (1999): 19-40. <http://eudml.org/doc/11502>.

@article{Mitov1999,
abstract = {This work is supported by Bulgarian NFSI, grant No. MM–704/97The 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.},
author = {Mitov, Kosto},
journal = {Serdica Mathematical Journal},
keywords = {Alternating Renewal Processes; Regenerative Processes; Limit Theorems; Branching Processes; State-Dependent Immigration; alternating renewal processes; regenerative processes; limit theorems; branching processes; state-dependent immigration},
language = {eng},
number = {1},
pages = {19-40},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Limit Theorems for Regenerative Excursion Processes},
url = {http://eudml.org/doc/11502},
volume = {25},
year = {1999},
}

TY - JOUR
AU - Mitov, Kosto
TI - Limit Theorems for Regenerative Excursion Processes
JO - Serdica Mathematical Journal
PY - 1999
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 25
IS - 1
SP - 19
EP - 40
AB - This work is supported by Bulgarian NFSI, grant No. MM–704/97The 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.
LA - eng
KW - Alternating Renewal Processes; Regenerative Processes; Limit Theorems; Branching Processes; State-Dependent Immigration; alternating renewal processes; regenerative processes; limit theorems; branching processes; state-dependent immigration
UR - http://eudml.org/doc/11502
ER -