Phase-lock-loop statistics without recourse to Fokker-Planck techniques

To obtain the steady-state probability distribution of the phase error for a phase-lock loop driven by the sum of modulated carrier and narrowband stationary noise, a familiarity with Fokker-Planck techniques is usually a prerequisite to formulate a differential equation that has the required distribution as its solution. Here a simpler treatment is offered, which uses the more standard tools of probability theory. The distribution of the frequency error is also considered.