ON SOME FUNCTIONALS OF BROWNIAN-MOTION WI TH APPLICATIONS TO WINDING PROPERTIES OF PLANAR BROWNIAN CURVES AND TO TRANSPORT-PROPERTIES OF ONE-DIMENSIONAL DIFFUSION IN RANDOM-MEDIA

This paper deals with functionals of Brownian motion that appear in va rious contexts, and with some properties of anomalous diffusion in a o ne-dimensional random environment. Section 2 explains why path integra ls provide a powerful framework to compute probability distribution of functionals of Brownian motion. This approach is used to study windin g properties of planar Brownian motion. Section 3 is devoted to an exp onential functional of Brownian motion, which arise in particular in t he study of transport properties of classical diffusion in a one-dimen sional disordered system of finite length. This functional belongs to the field of multiplicative stochastic processes.