The classical description of stimulated emission is that an electron can absorb a photon (with a probability associated with the Einstein absorption coefficient). One of two things may then happen:
Either the electron spontaneously and isotropically re-emits a photon. This is referred to as spontaneous emission which occurs with a certain probability associated with a time constant. Since the electron is free (not bound to an atom), the absorption of the photon is coupled to an energy continuum in the electron's phase space. As a result the electron may re-emit a photon in a different state from the incident photon.
Or the electron collides with another photon causing the emission of twin photons This is referred to as stimulated emission and is the hypothesis that needs to be tested. According to the Einstein coefficients, this re-emission should be significantly preponderant over spontaneous emission.