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

   
@article{EJP3049,
	author = {Romuald Elie and Mathieu Rosenbaum and Marc Yor},
	title = {On the expectation of normalized Brownian functionals up to first hitting times},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {19},
	year = {2014},
	keywords = {Brownian motion, hitting times, scaling, random sampling, Bessel process, Brownian meander, Ray-Knight theorem, Feynman-Kac formula.},
	abstract = {Let $B$ be a Brownian motion and $T_1$ its first hitting time of the level $1$. For $U$ a uniform random variable independent of $B$, we study in depth the distribution of $B_{UT_1}/\sqrt{T_1}$, that is the rescaled Brownian motion sampled at uniform time. In particular, we show that this variable is centered.},
	pages = {no. 37, 1-23},
	issn = {1083-6489},
	doi = {10.1214/EJP.v19-3049},    
        url = {http://ejp.ejpecp.org/article/view/3049}}