Abstract
The first two sections are devoted to the basic concepts on stationary Gaussian processes. These concepts are then used to deduce Rice's solution (1958) for the expected number per unit time of b up-crossings of the random surface elevation (with b being any fixed threshold). The chapter goes on to show three corollaries of this solution, including the distribution of wave height under narrowband assumption. Then, the chapter shows some important consequences of the quasi-determinism theory on wave statistics. The conclusive part of the chapter deals with the calculation of the maximum expected wave in a sea state of given significant wave height, duration, and shape of the spectrum. Three FORTRAN programs useful for this calculation are supplied and discussed. A fresh point of view (2013) of an old subject (wave height distribution: bandwidth and third-order nonlinearity effects) is dealt with in the conclusion to the chapter.
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