Fermionic path integration and Grassmann Brownian motion (Q1101772)

A Grassmann probability theory, with anticommuting random variables and stochastic processes, is developed using an extension of Berezin integration to infinite dimensional spaces. A Kolmogorov-type consistency condition allows integration on spaces of paths in anticommuting space. One particular stochastic process, Grassmann Brownian motion, is described and the associated measure used to give a path-integral formula for the kernel of the evolution operator in fermionic quantum mechanics. The Fourier mode expansion of Grassmann Brownian motion is derived.