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

Authors
  • Elie, Romuald
  • Rosenbaum, Mathieu
  • Yor, Marc
Publication Date
Jan 01, 2014
Source
HAL-ENAC
Keywords
Language
English
License
Unknown
External links

Abstract

Let B be a Brownian motion and T1 its first hitting time of the level 1. For U a uniform random variable independent of B, we study in depth the distribution of B UT1/√T1, that is the rescaled Brownian motion sampled at uniform time. In particular, we show that this variable is centered.

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