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We consider a branching random walk in a random space-time environment ofdisasters where each particle is killed when meeting a disaster. This extendsthe model of the "random walk in a disastrous random environment" introduced by[15]. We obtain a criterion for positive survival probability, see Theorem 1.The proofs for the subcritical and the supercritical cases follow standardarguments, which involve moment methods and a comparison with an embeddedbranching process with i.i.d. offspring distributions. The proof of almost sureextinction in the critical case is more difficult and uses the techniques from[8]. We also show that, in the case of survival, the number of particles growsexponentially fast.

A branching random walk among disasters