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Branching random walk: Seneta-Heyde norming

by J.D.Biggins and
A.E.Kyprianou ).

In *Trees: Proceedings of a Workshop
held in Versailles June 14-16, 1995,*
eds B. Chauvin, S. Cohen, A. Rouault. Birkhäuser, Basel.
(1996), 31-50

1991 Mathematics Subject Classification: 60J80

## Abstract

In the discrete-time branching random walk, the martingale formed by
taking the Laplace transform of the $n$th generation point process is
known, for suitable values of the argument, to converge in $L_{1}$
under an $X\log X$ condition, and to converge to zero when this
moment condition fails. This paper examines the strategy used in
Biggins and Kyprianou (1996) to prove that,
when the $X\log X$ condition fails,
there exists a Seneta-Heyde
renormalisation of the martingale that converges in probability to a
non-trivial random variable. To bring out how the method works it
is first discussed in the context of the Galton-Watson process.
The paper is concluded by extending the
results to the case of the continuous-time Markov branching random
walk.

## Availability

postscript file
dvi file

See also the companion paper

Other publications by J.D. Biggins
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