The Annals of Probability
- Ann. Probab.
- Volume 45, Number 6A (2017), 3481-3534.
On the boundary of the support of super-Brownian motion
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.
Ann. Probab., Volume 45, Number 6A (2017), 3481-3534.
Received: December 2015
Revised: August 2016
First available in Project Euclid: 27 November 2017
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Mueller, Carl; Mytnik, Leonid; Perkins, Edwin. On the boundary of the support of super-Brownian motion. Ann. Probab. 45 (2017), no. 6A, 3481--3534. doi:10.1214/16-AOP1141. https://projecteuclid.org/euclid.aop/1511773657