  We study evolution equations of drift-diffusion type when various parameters
are random. Motivated by applications in pedestrian dynamics, we focus on the
case when the total mass is, due to boundary or reaction terms, not conserved.
After providing existence and stability for the deterministic problem, we
consider uncertainty in the data. Instead of a sensitivity analysis we propose
to measure functionals of the solution, so-called quantities of interest (QoI),
by involving scalarizing statistics. For these summarizing statistics we
provide probabilistic continuity results.
