  The Douglas Rachford algorithm is an algorithm that converges to a minimizer
of a sum of two convex functions. The algorithm consists in fixed point
iterations involving computations of the proximity operators of the two
functions separately. The paper investigates a stochastic version of the
algorithm where both functions are random and the step size is constant. We
establish that the iterates of the algorithm stay close to the set of solution
with high probability when the step size is small enough. Application to
structured regularization is considered.
