  We show how the scattering-into-cones and flux-across-surfaces theorems in Quantum Mechanics have very intuitive pathwise probabilistic versions based on some results by Carlen about large time behaviour of paths of Nelson diffusions. The quantum mechanical results can be then recovered by taking expectations in our pathwise statements. 
Scattering into Cones and Flux across Surfaces in Quantum Mechanics: a   Pathwise Probabilistic Approach