  In this work we investigate gradient estimation for a class of contracting
stochastic systems on a continuous state space. We find conditions on the
one-step transitions, namely differentiability and contraction in a Wasserstein
distance, that guarantee differentiability of stationary costs. Then we show
how to estimate the derivatives, deriving an estimator that can be seen as a
generalization of the forward sensitivity analysis method used in deterministic
systems. We apply the results to examples, including a neural network model.
