We deal with sensitivity analysis for performance characteristics of stochastic processes. We will address the finite/transient problem and the infinite/stationary problem. Specifically, we introduce a concept of measure valued differentiation, called weak $ \cal D $--derivative, where $ \cal D $ is an appropriately defined class of performance functions $g$, such that the derivative of the integral of $g$ with respect to the measure under consideration exists. Weak $ \cal D $--differentiation generalises the concept of weak differ entiation, and our approach (1) works uniformly on a predefined class of performance functions, (2) allows for a product rule of differentiation, that is, analysing the derivative of a measure immediately yields results for finite products of the mea sure. Weak $ \cal D $--differentiation can be applied to conditional measures, such as Markov kernels, as well and then clearly identifies the trade--off between the generality of performance classes that can be analysed and the generality of the classes of measures. We will discuss how one can go from finite horizon results to infinite horizon results. We will conclude with some remarks on estimation.