  We use anticommuting variables to study probability distributions of random
variables, that are solutions of Langevin's equation. We show that the
probability density always enjoys "worldpoint supersymmetry". The partition
function, however, may not. We find that the domain of integration can acquire
a boundary, that implies that the auxiliary field has a non-zero expectation
value, signalling spontaneous supersymmetry breaking. This is due to the
presence of "fermionic" zeromodes, whose contribution cannot be cancelled by a
surface term. This we prove by an explicit calculation of the regularized
partition function, as well as by computing the moments of the auxiliary field
and checking whether they satisfy the identities implied by Wick's theorem.
Nevertheless, supersymmetry manifests itself in the identities that are
satisfied by the moments of the scalar, whose expressions we can calculate,for
all values of the coupling constant. We also provide some quantitative
estimates concerning the visibility of supersymmetry breaking effects in the
identities for the moments and remark that the shape of the distribution of the
auxiliary field can influence quite strongly how easy it would be to mask them,
since the expectation value of the auxiliary field doesn't coincide with its
typical value.
