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Article Dans Une Revue Stochastic Processes and their Applications Année : 2015

Growth rates of the population in a branching Brownian motion with an inhomogeneous breeding potential

E. Brunet
J.W. Harris
  • Fonction : Auteur
S.C. Harris
  • Fonction : Auteur
M.I. Roberts
  • Fonction : Auteur

Résumé

We consider a branching particle system where each particle moves as an independent Brownian motion and breeds at a rate proportional to its distance from the origin raised to the power p, for p is an element of [0, 2). The asymptotic behaviour of the right-most particle for this system is already known; in this article we give large deviations probabilities for particles following "difficult" paths, growth rates along "easy" paths, the total population growth rate, and we derive the optimal paths which particles must follow to achieve this growth rate

Dates et versions

hal-01164574 , version 1 (17-06-2015)

Identifiants

Citer

J. Berestycki, E. Brunet, J.W. Harris, S.C. Harris, M.I. Roberts. Growth rates of the population in a branching Brownian motion with an inhomogeneous breeding potential. Stochastic Processes and their Applications, 2015, 125 (5), pp.2096-2145. ⟨10.1016/j.spa.2014.12.008⟩. ⟨hal-01164574⟩
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