Borodin, A. N. On the distribution of functionals of Brownian motion stopped at the moment inverse the local time. (Russian) Zbl 0742.60073 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 184, 37-61 (1990). Let \(W_ x(t)\) be the Brownian motion, starting from the point \(x\), \(\ell(s,y)\) the Brownian local time, \[ {\mathfrak e}=\min\{s:\;\ell(s,u)=v\hbox{ or }\ell(s,z)=v\}. \] The author considers the integral functionals of Brownian motion and Brownian local time and the functionals \(\sup_{y\in R}\ell({\mathfrak e},y)\), \(\inf W_ x(t)\) and \(\sup W_ x(t)\) over the interval \([0,{\mathfrak e}]\). The Laplace transformations for joint and marginal distribution of such functionals are obtained. For some special cases the explicit formulas for the distribution are given, too. Reviewer: N.M.Zinchenko (Kiev) Cited in 1 ReviewCited in 4 Documents MSC: 60J65 Brownian motion 60J55 Local time and additive functionals 60J25 Continuous-time Markov processes on general state spaces Keywords:Markov process; Brownian motion; Brownian local time; integral functionals; Laplace transformations PDFBibTeX XMLCite \textit{A. N. Borodin}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 184, 37--61 (1990; Zbl 0742.60073) Full Text: EuDML