Examinando por Autor "Prat-Waldron, Arturo"

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    Asymptotics for the heat kernel in multicone domains
    (Academic Press Inc., 2016-02) Collet, Pierre; Duarte, Mauricio; Martínez, Servet; Prat-Waldron, Arturo; San Martín, Jaime
    A multicone domain Ω ⊆ Rn is an open, connected set that resembles a finite collection of cones far away from the origin. We study the rate of decay in time of the heat kernel p(t, x, y) of a Brownian motion killed upon exiting Ω, using both probabilistic and analytical techniques. We find that the decay is polynomial and we characterize limt→∞ t1+αp(t, x, y) in terms of the Martin boundary of Ω at infinity, where α > 0 depends on the geometry of Ω. We next derive an analogous result for tκ/2Px(T >t), with κ = 1 + α − n/2, where T is the exit time from Ω. Lastly, we deduce the renormalized Yaglom limit for the process conditioned on survival.