Let (B) be a (d)-dimensional Brownian motion, with (d geq 2) and (beta) defined as [d beta_{t}=frac{1}{left|B_{t}
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Let \(B\) be a \(d\)-dimensional Brownian motion, with \(d \geq 2\) and \(\beta\) defined as
\[d \beta_{t}=\frac{1}{\left\|B_{t}\right\|} B_{t} \cdot d B_{t}=\frac{1}{\left\|B_{t}\right\|} \sum_{i=1}^{d} B_{t}^{i} d B_{t}^{i}, \quad \beta_{0}=0\]
Prove that \(\beta\) is a Brownian motion. This will be the starting point of the study of Bessel processes.
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Related Book For
Mathematical Methods For Financial Markets
ISBN: 9781447125242
1st Edition
Authors: Monique Jeanblanc, Marc Yor, Marc Chesney
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