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

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  • Engländer, János

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.

Suggested Citation

  • Engländer, János, 2004. "Large deviations for the growth rate of the support of supercritical super-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 66(4), pages 449-456, March.
  • Handle: RePEc:eee:stapro:v:66:y:2004:i:4:p:449-456
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    Cited by:

    1. Ren, Yan-Xia & Song, Renming & Zhang, Rui, 2021. "The extremal process of super-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 137(C), pages 1-34.

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