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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