# Nonexplosion of a class of semilinear equations via branching particle representations

@article{Chakraborty2008NonexplosionOA, title={Nonexplosion of a class of semilinear equations via branching particle representations}, author={Santanu Chakraborty and Jos{\'e} Alfredo L{\'o}pez-Mimbela}, journal={Advances in Applied Probability}, year={2008}, volume={40}, pages={250 - 272} }

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 for x ∈ ℝ d , where A is the infinitesimal generator of a multiplicative semigroup and the pk s, k = 2, 3, …, are nonnegative functions such that We obtain sufficient conditions…

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