Limit theorems for sums determined by branching and other exponentially growing processes

Peter Jagers and Olle Nerman

Stochastic Processes and their Applications, 1984, vol. 17, issue 1, 47-71

Abstract: A branching process counted by a random characteristic has been defined as a process which at time t is the superposition of individual stochastic processes evaluated at the actual ages of the individuals of a branching population. Now characteristics which may depend not only on age but also on absolute time are considered. For supercritical processes a distributional limit theorem is proved, which implies that classical limit theorems for sums of characteristics evaluated at a fixed age point transfer into limit theorems for branching processes counted by these characteristics. A point is that, though characteristics of different individuals should be independent, the characteristics of an individual may well interplay with the reproduction of the latter. The result requires a sort of Lp-continuity for some 1 [less-than-or-equals, slant] p [less-than-or-equals, slant] 2. Its proof turns out to be valid for a wider class of processes than branching ones. For the case p = 1 a number of Poisson type limits follow and for p = 2 some normality approximations are concluded. For example results are obtained for processes for rare events, the age of the oldest individual, and the error of population predictions. This work has been supported by a grant from the Swedish Natural Science Research Council.

Keywords: branching; process; population; rare; event; prediction (search for similar items in EconPapers)
Date: 1984
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(84)90311-9
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:17:y:1984:i:1:p:47-71

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().