  We generalize Starobinskii's stochastic technique to the theory of a
massless, minimally coupled scalar interacting with a massless fermion in a
locally de Sitter geometry. The scalar is an ``active'' field that can engender
infrared logarithms. The fermion is a ``passive'' field that cannot cause
infrared logarithms but which can carry them, and which can also induce new
interactions between the active fields. The procedure for dealing with passive
fields is to integrate them out, then stochastically simplify the resulting
effective action following Starobinski\u{\i}. Because Yukawa theory is
quadratic in the fermion this can be done explicitly using the classic solution
of Candelas and Raine. We check the resulting stochastic formulation against an
explicit two loop computation. We also derive a nonperturbative, leading log
result for the stress tensor. Because the scalar effective potential induced by
fermions is unbounded below, back-reaction from this model might dynamically
cancel an arbitrarily large cosmological constant.
