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Nonexplosion of a class of semilinear equations via branching particle representations
2008
Advances in Applied Probability
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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 bypk,k= 2, 3, .... The corresponding branching process is related to the semilinear partial differential equationforx∈ ℝd, whereAis the infinitesimal generator of a multiplicative semigroup and thepks,k= 2, 3, ..., are nonnegative functions such thatWe obtain sufficient conditions for the
doi:10.1017/s0001867800002469
fatcat:7cypztpfonejtnsxr5vxkvhqre