Biane, Ph.; Le Gall, J. F.; Yor, M. Un processus qui ressemble au pont Brownien. (A process resembling the Brownian bridge). (French) Zbl 0621.60086 Sémin. probabilités XXI, Lect. Notes Math. 1247, 270-275 (1987). [For the entire collection see Zbl 0606.00022.] Let \((B_ t)\) be a real Brownian motion starting at 0 and \((\ell_ t,t\geq 0)\) its local time at 0, \(\tau_ t=\inf \{u:\ell_ u>t\}\). Put \(X_ u=B_{u\tau_ 1}/\sqrt{\tau_ 1}\), \(p(u)=\) Brownian bridge, and \(\lambda =\) its local time at level 0 at time 1. The main result asserts that, for each Borel functional \(F: C([0,1],{\mathbb{R}})\to {\mathbb{R}}_+\), one has the identity \[ E(F(X_ u,0\leq u\leq 1))=E(F(p(u),0\leq u\leq 1)\sqrt{2/\pi}/\lambda). \] Reviewer: U.Krengel Cited in 9 Documents MSC: 60J65 Brownian motion Keywords:Brownian bridge; Brownian motion; local time Citations:Zbl 0606.00022 PDFBibTeX XML Full Text: Numdam EuDML