  This paper studies nonstationary open dynamical systems from the statistical
viewpoint. By open, we mean that trajectories may escape through holes in the
phase space. By nonstationary, we mean that the dynamical model itself (as well
as the holes) may vary with time. Unlike the setting of random dynamical
systems, no assumptions are made about the statistics of this variability. We
formulate general results that yield conditional memory loss (an analog of
decay of correlations) at exponential rates for nonstationary open dynamical
systems. We apply our results to a class of nonstationary piecewise-smooth
expanding systems in higher dimension with moving holes.
