On the boundary of the support of super-Brownian motion

• Carl Mueller ^[1] ; Leonid Mytnik ^[2] ; Edwin Perkins ^[3]
  1. [1] University of Rochester

     University of Rochester

     City of Rochester, Estados Unidos

     
  2. [2] Technion – Israel Institute of Technology

     Technion – Israel Institute of Technology

     Israel

     
  3. [3] University of British Columbia

     University of British Columbia

     Canadá

     

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 6, 1, 2017, págs. 3481-3534
• Idioma: inglés
• DOI: 10.1214/16-AOP1141
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• Resumen

  • We study the density X(t,x)X(t,x) of one-dimensional super-Brownian motion and find the asymptotic behaviour of (...) as well as the Hausdorff dimension of the boundary of the support of X(t,⋅)X(t,⋅). The answers are in terms of the leading eigenvalue of the Ornstein–Uhlenbeck generator with a particular killing term. This work is motivated in part by questions of pathwise uniqueness for associated stochastic partial differential equations.