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arXiv · 1310.1181

On the expectation of normalized Brownian functionals up to first hitting times

Romuald Elie·Mathieu Rosenbaum·Marc Yor
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Abstract

Let B be a Brownian motion and T its first hitting time of the level 1. For U a uniform random variable independent of B, we study in depth the distribution of T^{-1/2}B_{UT}, that is the rescaled Brownian motion sampled at uniform time. In particular, we show that this variable is centered.

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Romuald Elie, Mathieu Rosenbaum, Marc Yor. 2013-10-04. On the expectation of normalized Brownian functionals up to first hitting times. https://arxiv.org/abs/1310.1181

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