On the boundary of the support of super-Brownian motion: with appendices

Carl Mueller; Leonid Mytnik; Edwin Perkins

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arXiv · 1512.08610

On the boundary of the support of super-Brownian motion: with appendices

Carl Mueller·Leonid Mytnik·Edwin Perkins

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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)<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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Carl Mueller, Leonid Mytnik, Edwin Perkins. 2015-12-29. On the boundary of the support of super-Brownian motion: with appendices. https://arxiv.org/abs/1512.08610

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