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This book examines multiple classes of random processes from the standpoints of statistical analysis, inference, and modeling. It describes several traditional models (fGn, fBm, mBm, ARFIMA, multiplicative cascades) and their appropriateness for modeling measured processes; offers brief discussions on ways to stimulate traditional processes and fit them to the data; and uses case studies to emphasize the real-life applicability of the subject matter. Accessible to anyone with a background in advanced calculus and algebra, this book is perfect for statisticians and engineers seeking a comprehensive introduction to an emerging field