Publication

Hausdorff dimension of the boundary of bubbles of additive Brownian motion and of the Brownian sheet

Robert Dalang, Thomas Mountford
2021
Journal Articles

Abstract

We first consider the additive Brownian motion process (X(s(1), s(2)), (s(1), s(2)) is an element of R-2) defined by X(s(1), s(2)) = Z(1)(s(1)) - Z2(s2), where Z(1) and Z(2) are two independent (two-sided) Brownian motions. We show that with probability 1, the Hausdorff dimension of the boundary of any connected component of the random set {(s(1,) s(2)) is an element of R-2 : X(s(1), s(2)) > 0} is equal to

Official source

https://infoscience.epfl.ch/entities/publication/349de3dd-be37-414c-88bd-e9b494e5e531

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Hausdorff dimension of the boundary of bubbles of additive Brownian motion and of the Brownian sheet

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