  Building on previous work on the stochastic analysis for Grassmann random
variables, we introduce a forward-backward stochastic differential equation
(FBSDE) which provides a stochastic quantisation of Grassmann measures. Our
method is inspired by the so-called continuous renormalisation group, but
avoids the technical difficulties encountered in the direct study of the flow
equation for the effective potentials. As an application, we construct a family
of weakly coupled subcritical Euclidean fermionic field theories and prove
exponential decay of correlations.
