# Limit Theorems for Regenerative Excursion Processes

Serdica Mathematical Journal (1999)

- Volume: 25, Issue: 1, page 19-40
- ISSN: 1310-6600

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topMitov, 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 -

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