On Bougerol and Dufresne's identities for exponential Brownian functionals (Q1283165)

The note contains several new distributional identities involving exponential functionals of the Brownian motion \(B=(B_t)\) and closely related with results by Bougerol and Dufresne. E.g., it is shown that the distribution of the following two-dimensional random vectors coincide: \(({\mathbf e}e^{-B_t}A_t,B_t)\) and \((\cosh(|B_t|+L_t),B_t)\) where \(A_t=\int_0^te^{2B_s}ds\), \(L\) is the local time of \(B\) at zero, and \({\mathbf e}\) is an exponential random variable independent of \(B\).