Lecture
Hausdorff Dimension and Brownian Motion
Description
This lecture covers the concept of Hausdorff dimension applied to the set of instants where Brownian motion is zero, showing that the dimension is 1/2. The instructor explains the construction of coverings for the set of zeros, demonstrating that the dimension is less than 1/2. Through examples involving intervals and Cantor sets, the lecture illustrates how to estimate the dimension of sets with non-integer values. The application of the Hausdorff dimension to Brownian motion leads to the theorem that the set of zeros has a dimension of 1/2 with probability 1. The lecture concludes with a proof that the dimension is less than 1/2 with probability 1 for a specific interval, setting the stage for further exploration.
Instructors (2)
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Ontological neighbourhood
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