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Large Deviations for the Growth Rate of the Support of Supercritical Super-Brownian Motion

János Engländer

出版	SSRN, 2018
URL	http://books.google.com.hk/books?id=Vzf-zgEACAAJ&hl=&source=gbs_api

註釋

We prove a large deviation result for the growth rate of the support of the -dimensional (strictly dyadic) branching Brownian motion and the -dimensional (supercritical) super-Brownian motion . We show that the probability that () remains in a smaller than typical ball up to time is exponentially small in and we compute the cost function. The cost function turns out to be the same for and . 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 , first obtained by Pinsky by pde methods.