We associate with the Grassmann algebra a topological algebra of distributions, which allows the study of processes analogous to the corresponding free stochastic processes with stationary increments, as well as their derivatives.
D. Alpay, I. L. Paiva, and D. C. Struppa, "Distribution spaces and a new construction of stochastic processes associated with the Grassmann algebra," J. Math. Phys. 60(1), 013508 (2019). https://doi.org/10.1063/1.5052010