2015/12/29 by Carl Mueller, Mueller, Carl, Leonid Mytnik +3
Mathematics · #35K15 (secondary) #60H15 #60J68 (primary) #FOS: Mathematics #Probability (math.PR) #math.PR #msc:35K15 #msc:60H15 #msc:60J68
paper · pdf · doi:10.48550/arxiv.1512.08610
64 pages
arxiv created 2015/12/29 · arxiv updated 2015/12/31
We study the density X(t,x) of one-dimensional super-Brownian motion and find the asymptotic behaviour of P(0<X(t,x)<a) as a approaches 0, as well as the Hausdorff dimension of the boundary of the support of X(t). The answers are in terms of the lead 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.