  Blind source separation (BSS) aims to recover an unobserved signal $S$ from
its mixture $X=f(S)$ under the condition that the effecting transformation $f$
is invertible but unknown. As this is a basic problem with many practical
applications, a fundamental issue is to understand how the solutions to this
problem behave when their supporting statistical prior assumptions are
violated. In the classical context of linear mixtures, we present a general
framework for analysing such violations and quantifying their impact on the
blind recovery of $S$ from $X$. Modelling $S$ as a multidimensional stochastic
process, we introduce an informative topology on the space of possible causes
underlying a mixture $X$, and show that the behaviour of a generic BSS-solution
in response to general deviations from its defining structural assumptions can
be profitably analysed in the form of explicit continuity guarantees with
respect to this topology. This allows for a flexible and convenient
quantification of general model uncertainty scenarios and amounts to the first
comprehensive robustness framework for BSS. Our approach is entirely
constructive, and we demonstrate its utility with novel theoretical guarantees
for a number of statistical applications.
