Using a combined ray tracing and Fokker-Planck code, an investigation is made on the propagation and absorption of the launched power spectrum during lower hybrid (LH) current drive in tokamaks, in a situation where toroidally induced ray stochasticity is important. Stochastic effects are correctly taken into account by tracing a large number of rays. The influence of the balance between the wave damping and the stochastic divergence of nearby ray trajectories in governing the power spectrum dynamics and in establishing the characteristics of the LH power deposition patterns is illustrated. It is shown that, when strong wave damping prevails, the launched power spectrum behaves regularly: the LH power deposition is localized and the absorbed power spectrum is very similar in shape to the launched one, although some broadening and shifting in the parallel wave index generally occur. If the wave damping is weak and stochastic effects are important, the rays end by covering the entire plasma cross-section and the power spectrum dynamics follows a diffusive pattern: the LH power deposition turns out to be extended and the absorbed power spectrum is much broader than the launched one, as a result of strong spreading towards the high absolute values of the parallel wave index