On the asymptotic behaviour of discrete time stochastic growth processes

Keller G, Kersting G, Rösler U (1987)

Publication Type: Journal article, Original article

Publication year: 1987

Journal

Annals of Probability Institute of Mathematical Statistics (IMS)

Publisher: Institute of Mathematical Statistics (IMS)

Book Volume: 15

Pages Range: 305--343

Journal Issue: 1

URI: http://links.jstor.org/sici?sici=0091-1798(198701)15:1<305:OTABOD>2.0.CO;2-B&origin=MSN

Abstract

We study the asymptotic behaviour of the solution of the stochastic difference equation Xn+1=Xn+g(Xn)(1+ξn+1), where g is a positive function, (ξn) is a 0-mean, square-integrable martingale difference sequence, and the states Xn<0 are assumed to be absorbing. We clarify, under which conditions Xn diverges with positive probability, satisfies a law of large numbers, and, properly normalized, converges in distribution. Controlled Galton-Watson processes furnish examples for the processes under consideration.

Authors with CRIS profile

Gerhard Keller Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

Goethe-Universität Frankfurt am Main DE Germany (DE) Christian-Albrechts-Universität zu Kiel DE Germany (DE)

How to cite

APA:

Keller, G., Kersting, G., & Rösler, U. (1987). On the asymptotic behaviour of discrete time stochastic growth processes. Annals of Probability, 15(1), 305--343.

MLA:

Keller, Gerhard, Götz Kersting, and Uwe Rösler. "On the asymptotic behaviour of discrete time stochastic growth processes." Annals of Probability 15.1 (1987): 305--343.

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