We present an approach for initiating and tracing ultra-fast electron
dynamics in core-excited atoms, molecules and solids. The approach is based on
stimulated resonant inelastic x-ray scattering induced by a single, chirped,
broadband XUV/x-ray pulse. A first interaction with this pulse prepares a
core-excited state wave packet by resonant core-excitation. A second
interaction with the pulse at a later time induces the transition to
valence-excited states which is associated with stimulated emission. The
preparation of the core-excited wave packet and the transition from the
core-excited states to the valence-excited states occur at distinct
chirp-dependent times. As a consequence, the stimulated emission carries
information about the time evolution of the core-excited state wave packet
