  We explain how stochastic TQFT supersymmetry can be made compatible with
space supersymmetry. Taking the case of N=2 supersymmetric quantum mechanics,
(the proof would be the same for the Wess-Zumino model), we determine the
kernels that ensure the convergence of the stochastic process toward the
standard path integral, under the condition that they are covariant under
supersymmetry. They depend on a massive parameter M that can be chosen at will
and modifies the course of the stochastic evolution, but the infinite
stochastic time limit of the correlation functions is in fact independent on
the choice of M.
