Asymptotics for the heat kernel in multicone domains
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Archivos
Fecha
2016-02
Profesor/a Guía
Facultad/escuela
Idioma
en
Título de la revista
ISSN de la revista
Título del volumen
Editor
Academic Press Inc.
Nombre de Curso
Licencia CC
Licencia CC
Resumen
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.
Notas
Indexación: Scopus.
Palabras clave
Heat Kernel, Brownian Motion, Yaglom Limit, Martin Boundary
Citación
Journal of Functional Analysis. Volume 270, Issue 4, Pages 1269 - 1298. 15 February 2016
DOI
10.1016/j.jfa.2015.10.021