On the Existence of Self-Intersections for Quasi-Every Brownian Path in Space
On the Existence of Self-Intersections for Quasi-Every Brownian Path in Space
The set of self-intersections of a Brownian path $b(t)$ taking values in $\mathbb{R}^3$ has Hausdorff dimension 1, for almost every such path, with respect to Wiener measure, a result due to Fristedt. Here we prove that this result (together with the corresponding result for paths in $\mathbb{R}^2$) in fact holds …