Global Asymptotic Stability of Solutions of Nonautonomous Master Equations

We wish to generalize van Kampen’s theorem to include nonautonomous master equations. Such a theorem is important in applications, e.g. in ion channel kinetics, where subunit opening and closing rates are subject to external forces (e.g. membrane voltage) and are therefore often unavoidably nonautonomous. There are two issues to consider when moving to the nonautonomous case. The first is that, in general, nonautonomous master equations may have no stationary distributions. For example, take