Abstract
We study the density $X(t,x)$ of one-dimensional super-Brownian motion and find the asymptotic behaviour of $P(0<X(t,x)\le a)$ as $a\downarrow0$ as well as the Hausdorff dimension of the boundary of the support of $X(t,\cdot)$. 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.
Citation
Carl Mueller. Leonid Mytnik. Edwin Perkins. "On the boundary of the support of super-Brownian motion." Ann. Probab. 45 (6A) 3481 - 3534, November 2017. https://doi.org/10.1214/16-AOP1141
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