Multistage stochastic programs are regarded as mathematical programs in a Banach space X of summable functions. Relying on a result for parametric programs in Banach spaces, the paper presents conditions under which linearly constrained convex multistage problems behave stably when the (input) data process is subjected to (small) perturbations. In particular, the authors show the persistence of optimal solutions, the local Lipschitz continuity of the optimal value and the upper semicontinuity of optimal sets with respect to the weak topology in X. The linear case with deterministic first-stage decisions is studied in more detail.
