The Annals of Probability

On the boundary of the support of super-Brownian motion

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.

Article information

Source
Ann. Probab., Volume 45, Number 6A (2017), 3481-3534.

Dates
Revised: August 2016
First available in Project Euclid: 27 November 2017

https://projecteuclid.org/euclid.aop/1511773657

Digital Object Identifier
doi:10.1214/16-AOP1141

Mathematical Reviews number (MathSciNet)
MR3729608

Zentralblatt MATH identifier
06838100

Citation

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

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