Regularity and irregularity of \bolds(1+β)-stable super-Brownian motion

• Leonid Mytnik ^[1] ; Edwin Perkins ^[2]
  1. [1] Technion – Israel Institute of Technology

     Technion – Israel Institute of Technology

     Israel

     
  2. [2] University of British Columbia

     University of British Columbia

     Canadá

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 31, Nº. 3, 2003, págs. 1413-1440
• Idioma: inglés
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• Resumen

  • This paper establishes the continuity of the density of (1+β)-stable super-Brownian motion (0<β<1) for fixed times in d=1, and local unboundedness of the density in all higher dimensions where it exists. We also prove local unboundedness of the density in time for a fixed spatial parameter in any dimension where the density exists, and local unboundedness of the occupation density (the local time) in the spatial parameter for dimensions d≥2 where the local time exists.