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

  • A. E. Kyprianou (a1)

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.

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Corresponding author

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

References

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