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

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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.
Original languageEnglish
Pages (from-to)795-802
Number of pages8
JournalJournal of Applied Probability
Volume35
Issue number4
DOIs
Publication statusPublished - 1998

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Branching Random Walk
Uniqueness of Solutions
Traveling Wave Solutions
Functional equation
Context
Communication
Random walk
Uniqueness
Traveling wave solutions

Cite this

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title = "Slow variation and uniqueness of solutions to the functional equation in the branching random walk",
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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AB - 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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