Limit Theorems for Weakly Subcritical Branching Processes in Random Environment

V. I. Afanasyev (), C. Böinghoff (), G. Kersting () and V. A. Vatutin ()
Additional contact information
V. I. Afanasyev: Steklov Mathematical Institute
C. Böinghoff: Universität Frankfurt
G. Kersting: Universität Frankfurt
V. A. Vatutin: Steklov Mathematical Institute

Journal of Theoretical Probability, 2012, vol. 25, issue 3, 703-732

Abstract: Abstract For a branching process in random environment, it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the process may at the same time be subcritical and, conditioned on nonextinction, “supercritical.” This so-called weakly subcritical case is considered in this paper. We study the asymptotic survival probability and the size of the population conditioned on nonextinction. Also a functional limit theorem is proved, which makes the conditional supercriticality manifest. A main tool is a new type of functional limit theorems for conditional random walks.

Keywords: Branching process; Random environment; Random walk; Change of measure; Survival probability; Functional limit theorem; 60J80; 60G50; 60F17 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-010-0331-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:jotpro:v:25:y:2012:i:3:d:10.1007_s10959-010-0331-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-010-0331-6

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().