Título
Self-Similar Stable Processes Arising from High-Density Limits of Occupation Times of Particle Systems
Autor
LUIS GABRIEL GOROSTIZA Y ORTEGA
Nivel de Acceso
Acceso Abierto
Materias
Resumen o descripción
We extend results on time-rescaled occupation time fluctuation limits of
the (d, α, β)-branching particle system (0 < α ≤ 2, 0 < β ≤ 1) with Poisson initial
condition. The earlier results in the homogeneous case (i.e., with Lebesgue initial
intensity measure) were obtained for dimensions d > α/β only, since the particle
system becomes locally extinct if d ≤ α/β. In this paper we show that by introducing
high density of the initial Poisson configuration, limits are obtained for all dimensions,
and they coincide with the previous ones if d > α/β.We also give high-density
limits for the systems with finite intensity measures (without high density no limits
exist in this case due to extinction); the results are different and harder to obtain
due to the non-invariance of the measure for the particle motion. In both cases, i.e.,
Lebesgue and finite intensity measures, for low dimensions [d < α(1 + β)/β and d <
α(2 + β)/(1 + β), respectively] the limits are determined by non-Lévy self-similar
stable processes. For the corresponding high dimensions the limits are qualitatively
different: S
(Rd
)-valued Lévy processes in the Lebesgue case, stable processes
constant in time on (0,∞) in the finite measure case. For high dimensions, the laws of
all limit processes are expressed in terms of Riesz potentials. If β = 1, the limits are
Gaussian. Limits are also given for particle systems without branching, which yields
Editor
Springer Verlag
Fecha de publicación
2008
Tipo de publicación
Artículo
Versión de la publicación
Versión publicada
Recurso de información
Formato
application/pdf
Idioma
Inglés
Audiencia
Investigadores
Repositorio Orígen
Repositorio Institucional CIMAT
Descargas
307