Optimal survival strategy for branching Brownian motion in a Poissonian trap field

@article{Oz2019OptimalSS,
  title={Optimal survival strategy for branching Brownian motion in a Poissonian trap field},
  author={Mehmet Oz and J'anos Englander},
  journal={Annales de l'Institut Henri Poincar{\'e}, Probabilit{\'e}s et Statistiques},
  year={2019}
}
  • Mehmet Oz, J. Englander
  • Published 26 October 2017
  • Mathematics
  • Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
We study a branching Brownian motion Z with a generic branching law, evolving in Rd, where a field of Poissonian traps is present. Each trap is a ball with constant radius. We focus on two cases of Poissonian fields: a uniform field and a radially decaying field. Using classical results on the convergence of the speed of branching Brownian motion, we establish precise results on the population size of Z, given that it avoids the trap field, while staying alive up to time t. The results are… 

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