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

Author

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  • Berestycki, Julien
  • Brunet, Éric
  • Harris, John W.
  • Harris, Simon C.
  • Roberts, Matthew I.

Abstract

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∈[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.

Suggested Citation

  • Berestycki, Julien & Brunet, Éric & Harris, John W. & Harris, Simon C. & Roberts, Matthew I., 2015. "Growth rates of the population in a branching Brownian motion with an inhomogeneous breeding potential," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 2096-2145.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:5:p:2096-2145
    DOI: 10.1016/j.spa.2014.12.008
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    References listed on IDEAS

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    1. Hardy, Robert & Harris, Simon C., 2006. "A conceptual approach to a path result for branching Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1992-2013, December.
    2. Berestycki, J. & Brunet, É. & Harris, J.W. & Harris, S.C., 2010. "The almost-sure population growth rate in branching Brownian motion with a quadratic breeding potential," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1442-1446, September.
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