Lefebvre, Mario et Léonard, Éric, On the first hitting place of the integrated Wiener process, Advances in applied probability , 21(4), 1989, pp. 945-948
Let dx(t) = y(t) dt, where y(t) is a one-dimensional Wiener process. In this note, we obtain a formula for the moment-generating function of y(T), where T is the 1/2-winding time about the origin of the integrated Wiener process x(t).