Journal of Applied Probability

Asymptotic behaviour near extinction of continuous-state branching processes

Gabriel Berzunza and Juan Carlos Pardo

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Abstract

In this paper we study the asymptotic behaviour near extinction of (sub-)critical continuous-state branching processes. In particular, we establish an analogue of Khintchine's law of the iterated logarithm near extinction time for a continuous-state branching process whose branching mechanism satisfies a given condition.

Article information

Source
J. Appl. Probab., Volume 53, Number 2 (2016), 381-391.

Dates
First available in Project Euclid: 17 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.jap/1466172861

Mathematical Reviews number (MathSciNet)
MR3514285

Zentralblatt MATH identifier
1344.60080

Subjects
Primary: 60G17: Sample path properties
Secondary: 60G51: Processes with independent increments; Lévy processes 60G80

Keywords
Continuous-state branching process Lamperti transform Lévy process conditioning to stay positive rate of growth

Citation

Berzunza, Gabriel; Pardo, Juan Carlos. Asymptotic behaviour near extinction of continuous-state branching processes. J. Appl. Probab. 53 (2016), no. 2, 381--391. https://projecteuclid.org/euclid.jap/1466172861


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