  We discuss a wide class of time inhomogeneous quantum evolution which is
represented by two-parameter family of completely positive trace-preserving
maps. These dynamical maps are constructed as infinite series of jump
processes. It is shown that such dynamical maps satisfy time inhomogeneous
memory kernel master equation which provides a generalization of the master
equation involving the standard convolution. Time-local (time convolution-less)
approach is discussed as well. Finally, the comparative analysis of traditional
time homogeneous vs. time inhomogeneous scenario is provided.
