Brownian Motion and Dimension of Perfect Sets
Brownian Motion and Dimension of Perfect Sets
Let X(t) denote real-valued Brownian motion on the interval 0 ≦ t ≦ 1, so normalized that E(X 2 (t)) = t. We prove some theorems about transforms X(F) of closed sets F: in general, F is not known in advance but depends on X. The main point of comparison …