Multi-scale Clustering for a Non-Markovian Spatial Branching Process View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2005-10

AUTHORS

Klaus Fleischmann, Vladimir A. Vatutin

ABSTRACT

Consider a system of particles which move in Rd according to a symmetric α-stable motion, have a lifetime distribution of finite mean, and branch with an offspring law of index 1+β. In case of the critical dimension d=α/β the phenomenon of multi-scale clustering occurs. This is expressed in an fdd scaling limit theorem, where initially we start with an increasing localized population or with an increasing homogeneous Poissonian population. The limit state is uniform, but its intensity varies in line with the scaling index according to a continuous-state branching process of index 1+β. Our result generalizes the case α=2 of Brownian particles of Klenke (1998), where p.d.e. methods had been used which are not available in the present setting. More... »

PAGES

719-755

References to SciGraph publications

  • 1998-01. Limit Processes for Age-Dependent Branching Particle Systems in JOURNAL OF THEORETICAL PROBABILITY
  • 1994-12. Diffusive clustering in an infinite system of hierarchically interacting diffusions in PROBABILITY THEORY AND RELATED FIELDS
  • 1974. Functional Analysis in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10959-005-7524-4

    DOI

    http://dx.doi.org/10.1007/s10959-005-7524-4

    DIMENSIONS

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