Mathematical Preliminaries: Elements of Probability Theory and Random Functions

For easiness of reference and for readers convenience, we present here a brief recapitulation of elements of probability theory and of theory of random functions needed in this book. This subject is covered by many text books. A handy reference for introduction to probability theory is, for instance, Mood & Graybill (1963). For the theory of random functions one may consult the books by Papoulis (1965) and Yaglom (1962), or the monograph of Matheron (1965), which is close in spirit with the material presented herein. Recent texts oriented toward hydrologic applications are Bras and Rodriguez-Iturbe (1985) and Vanmarcke (1983).