'Stimulation of photon emission'
An interaction of a photon with a free electron emits a low energy photon in the same direction as the incident photon. The electron energy and momentum is unchanged by the collision and the other emitted photon is not changed in direction from the incident photon but has energy less by the amount of energy of the induced 2nd photon. Assuming a collision rate of once in many Mpc the successive reddening of the source photon would resemble the light from observed objects (that redden with distance).
The question of why starlight appears to redden with increasing distance of the source has a de facto accepted answer, namely that the Big Bang has been stretching the space that photons have been in since they were emitted. The CMB, another prominent and uniform observational feature, is also fully explained by a universe becoming transparent as atoms form once the heat of the Big Bang has cooled below a threshold and photons are released and stretched by expanding space.
It is striking that both features are apparently virtually homogeneous *and* they are complimentary in the sense that photons of CMB are low energy while reddening photons regularly lose small amounts of energy apparently continuously (not *quantumly*) over considerable distances.
A single alternative mechanism can replicate some important features of both stellar reddening and CMB. A single type of collision event is postulated that reoccurs randomly with a characteristic distance (time) constant and that produces both starlight reddening and CMB as a consequence of each other.
That is, reddened starlight equals starlight minus shed CMB photons.