Limits of Applicability of the Theory — Caveat Reader

For the introduction of the probability density function, Fig. 3.1(a) shows an ensemble of random time functions. These random time functions are realizations of a stochastic process. In practice, usually just one realization is measured, thus averaging is performed as averaging in time – which means that time averages are assumed to be equal to ensemble averages. In this case, the process is called ergodic (see page 43).