The Hausdorff dimension of the double points on the Brownian frontier
Richard Kiefer, Peter Morters
TL;DR
This paper determines the Hausdorff dimension of the set of double points on the frontier of a planar Brownian motion, advancing understanding of the geometric complexity of Brownian paths.
Contribution
It provides the first precise calculation of the Hausdorff dimension of double points on the Brownian frontier, a previously unresolved geometric property.
Findings
Hausdorff dimension of double points on the frontier is explicitly calculated
The result enhances understanding of the geometric structure of Brownian motion
The study bridges stochastic processes and fractal geometry
Abstract
The frontier of a planar Brownian motion is the boundary of the unbounded component of the complement of its range. In this paper we find the Hausdorff dimension of the set of double points on the frontier.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Stochastic processes and statistical mechanics · Stochastic processes and financial applications