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A probabilistic proof of non-explosion of a non-linear PDE system
Published online by Cambridge University Press: 14 July 2016
Abstract
Using a representation in terms of a two-type branching particle system, we prove that positive solutions of the system remain bounded for suitable bounded initial conditions, provided A and B generate processes with independent increments and one of the processes is transient with a uniform power decay of its semigroup. For the case of symmetric stable processes on R1,this answers a question raised in [4].
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- Copyright © Applied Probability Trust 2000
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