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November 2017 On the boundary of the support of super-Brownian motion
Carl Mueller, Leonid Mytnik, Edwin Perkins
Ann. Probab. 45(6A): 3481-3534 (November 2017). DOI: 10.1214/16-AOP1141

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.

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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

Information

Received: 1 December 2015; Revised: 1 August 2016; Published: November 2017
First available in Project Euclid: 27 November 2017

zbMATH: 06838100
MathSciNet: MR3729608
Digital Object Identifier: 10.1214/16-AOP1141

Subjects:
Primary: 60H15 , 60J68
Secondary: 35K15

Keywords: Hausdorff dimension , Stochastic partial differential equations , Super-Brownian motion

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 6A • November 2017
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