Large deviations for the growth rate of the support of supercritical super-Brownian motion

János Engländer

Statistics & Probability Letters, 2004, vol. 66, issue 4, 449-456

Abstract: We prove a large deviation result for the growth rate of the support of the d-dimensional (strictly dyadic) branching Brownian motion Z and the d-dimensional (supercritical) super-Brownian motion X. We show that the probability that Z (X) remains in a smaller than typical ball up to time t is exponentially small in t and we compute the cost function. The cost function turns out to be the same for Z and X. In the proof we use a decomposition result due to Evans and O'Connell and elementary probabilistic arguments. Our method also provides a short alternative proof for the lower estimate of the large time growth rate of the support of X, first obtained by Pinsky by pde methods.

Keywords: Measure-valued; process; Superdiffusion; Super-Brownian; motion; Branching; Brownian; motion; Subcritical; wave; speed; Large; deviations; KPP-equation (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (1)

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