On the Existence of φ-Moments of the Limit of a Normalized Supercritical Galton–Watson Process

G. Alsmeyer and U. Rösler
Additional contact information
G. Alsmeyer: Fachbereich Mathematik, Westfälische Wilhelms-Universität Münster
U. Rösler: Christian-Albrechts-Universität Kiel

Journal of Theoretical Probability, 2004, vol. 17, issue 4, 905-928

Abstract: Abstract Let (Z n ) n≥ 0 be a supercritical Galton–Watson process with finite re-production mean μ and normalized limit W=lim n → ∞μ−n Z n . Let further φ: [0,∞) → [0,∞) be a convex differentiable function with φ(0)=φ′(0)=0 and such that φ( $$x^{1/2^n}$$ ) is convex with concave derivative for some n ≥ 0. By using convex function inequalities due to Topchii and Vatutin, and Burkholder, Davis and Gundy, we prove that 0

Keywords: Supercritical Galton–Watson process, convex function, regular variation, φ-moment; martingale, convex function inequality; Kesten-Stigum theorem (search for similar items in EconPapers)
Date: 2004
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-004-0582-1 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:17:y:2004:i:4:d:10.1007_s10959-004-0582-1

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

DOI: 10.1007/s10959-004-0582-1

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 ().