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On the boundary of the support of super-Brownian motion: with appendices
Carl Mueller, Leonid Mytnik, Edwin Perkins · 2015-12-29 · via math.PR updates on arXiv.org

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.

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