The modulation function has independent deterministic and random components. ISI describes the pulse distortions caused by the bandwidth limitations of the system. While all jitter components alter the measured symbol interval, DCD is a static deviation that is a function of difference between the propagation of signal rise and fall. Further modulation of the baseband signal is caused by the coupling of sinusoidal signals into the phase-locked loop circuit. Usually this modulation is from low frequency signals that sneak in through the power supply.
Random jitter is modeled as white noise.
An offset whose amplitude is picked from a zero-mean normal distribution is applied to each signal transition. The offsets are assumed to be independent, that is, the amplitude of the current offset is not influenced by the amplitudes of the preceding or following offsets. Random jitter is typically characterized by the standard deviation of the distribution from which the amplitudes are drawn. Given the probabilistic nature of random jitter, it is useful to also model deterministic jitter with a distribution function. The total jitter distribution then becomes the convolution of the deterministic and random distributions.