Please use this identifier to cite or link to this item: http://cimat.repositorioinstitucional.mx/jspui/handle/1008/925
NONEXPLOSION OF A CLASS OF SEMILINEAR EQUATIONS VIA BRANCHING PARTICLE REPRESENTATIONS
JOSE ALFREDO LOPEZ MIMBELA
Acceso Abierto
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Procesos de Branching
We consider a branching particle system where an individual particle gives birth to a random number of offspring at the place where it dies. The probability distribution of the number of offspring is given by pk, k = 2, 3, . . . . The corresponding branching process is related to the semilinear partial differential equation ∂u/∂t = Au(t, x) + ∞ k=2 pk(x)uk(t, x) for x ∈ Rd , whereAis the infinitesimal generator of a multiplicative semigroup and the pks, k = 2, 3, . . . , are nonnegative functions such that k pk = 1. We obtain sufficient conditions for the existence of global positive solutions to semilinear equations of this form. Our results extend previous work by Nagasawa and Sirao (1969) and others.
Cambridge University Press
2008
Artículo
Inglés
Investigadores
PROCESOS DE MARKOV
Versión publicada
publishedVersion - Versión publicada
Appears in Collections:Probababilidad Y Estadística

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