The successive hitting times for the integrated Brownian motion
Let \(B_t\) be the real Brownian motion, and \(X_t: =x+\int^t_0 (y+B_s)ds\). Set \(\tau_{n+1}: =\min \{t> \tau_n\mid X_t=0\}\) and \(\beta_n: =|B_{\tau_n} |\). The author computes the Kontorovich-Lebedev transform of \((\tau_n,\beta_n)\) in the two cases: \(\tau_0 =0\) or 1, and then deduces rather complicated formulas for the density of \((\tau_n, \beta_n)\), thereby completing an ancient article by H. P. McKean.
scientific article; zbMATH DE number 999601