Stationary stochastic processes. Theory and applications. (Q2919531)

This book has all the potential for a ``second course'' in stationary processes, presenting a broad view on the theory that lies behind many applications. The main focus lies on second-order properties and their close link to Fourier analysis, thereby mostly avoiding any more concrete weak (or strong) dependence concepts like Markov chains, mixing conditions or near-epoche dependence. A notable feature of this book is its treatment of spatial processes and spatial statistics, offering a nice wrap-up of excursion theory and level crossings, and thereby giving access and insight to material that is usually only available in more advanced and/or specialised texts. The structure of this book is as follows. Chapters one and two discuss and introduce basic sample function properties. Chapter three is exclusively devoted to spectral representation. Employing this concept, Chapters four and five discuss linear filters. Ergodic theory and some mixing concepts are presented in Chapter six. Chapter seven introduces random fields, while Chapter eight discusses level crossings and excursions. Each chapter ends with a set of exercises, complementing the preceding exposition. Additional material and some hints on selected exercises is given in the Appendices A--D.