A one-dimensional Brownian motion is a recurrent process, a Bessel process with index strictly greater than 0
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A one-dimensional Brownian motion is a recurrent process, a Bessel process with index strictly greater than 0 is a transient process. For the (recurrent) one-dimensional Brownian motion, the times \(T_{y}\) are large, i.e., \(\mathbb{E}_{x}\left(T_{y}^{\alpha}\right)<\infty\), for \(x eq y\) if and only if \(\alpha<1 / 2\).
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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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