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Supercritical super-brownian motion with a general branching mechanism and travelling waves

A. E. Kyprianou, R.-L. Liu, A. Murillo-Salas, Y.-X. Ren (2012)

Annales de l'I.H.P. Probabilités et statistiques

We offer a probabilistic treatment of the classical problem of existence, uniqueness and asymptotics of monotone solutions to the travelling wave equation associated to the parabolic semi-group equation of a super-Brownian motion with a general branching mechanism. Whilst we are strongly guided by the reasoning in Kyprianou (Ann. Inst. Henri Poincaré Probab. Stat.40 (2004) 53–72) for branching Brownian motion, the current paper offers a number of new insights. Our analysis incorporates the role...

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