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Slow variation and uniqueness of solutions to the functional equation in the branching random walk

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

A. E. Kyprianou
A. E. Kyprianou*
Affiliation:
The London School of Economics
*
∗Postal address: Department of Mathematics and Statistics, University of Edinburgh, James Clerk Maxwell Building, Mayfield Road, Edinburgh, EH9 3JZ, Scotland. Email address: andreas@maths.ed.ac.uk
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Abstract

In this short communication, some of the recent results of Liu (1998) and Biggins and Kyprianou (1997), concerning solutions to a certain functional equation associated with the branching random walk, are strengthened. Their importance is emphasized in the context of travelling wave solutions to a discrete version of the KPP equation and the connection with the behaviour of the rightmost particle in the nth generation.

Keywords

Branching random walkfunctional equationsmartingalesKPP equationtravelling wave solutions

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 4 , December 1998 , pp. 795 - 801
Copyright
Copyright © Applied Probability Trust 1998 

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