  We show a decomposition into the sum of a martingale and a deterministic
quantity for time averages of the solutions to non-autonomous SDEs and for
discrete-time Markov processes. In the SDE case the martingale has an explicit
representation in terms of the gradient of the associated semigroup or
transition operator. We show how the results can be used to obtain quenched
Gaussian concentration inequalities for time averages and to provide insights
into the Averaging principle for two-timescale processes.
