Stochastic Processes

The book presents, for the first time, a detailed analysis of harmonizable processes and fields (in the weak sense) that contain the corresponding stationary theory as a subclass. It also gives the structural and some key applications in detail. These include Levy's Brownian motion, a probabilistic proof of the longstanding Riemann's hypothesis, random fields indexed by LCA and hypergroups, extensions to bistochastic operators, Cramér–Karhunen classes, as well as bistochastic operators with some statistical applications.The material is accessible to graduate students in probability and statistics as well as to engineers in theoretical applications. There are numerous extensions and applications pointed out in the book that will inspire readers to delve deeper.Contents: Harmonizability and Stochastic AnalysisHarmonic Approaches for Integrable ProcessesApplications and Extensions of Harmonizable ProcessesIsotropic Harmonizable Fields and ApplicationsHarmonizable Fields on Groups and HypergroupsSome Extensions of Harmonizable Random Fields
Readership: Graduate students and researchers in probability and statistics interested in stochastic processes and harmonizable processes. Electrical-communication engineers as well as other applied professionals in these fields.Stochastic Processes;Harmonizable Classes;Harmonizable Processes;Harmonizable Theory;Nonstationary Process;Positive Definiteness;Probabilistic Proof of Riemann's Hypothesis;Integral Representations of (Gel'fand's) Local Functionals;Analysis of Bistochastic Operators;Weakly Stationary Processes;Structural and Integral Representations;Statistical Analysis;Including Works of Cramer, Karhunen, Rozanov, Kolmogorov, Doob, Loeve and Others0Key Features:The book covers harmonizable theory in detailThe research works contain detailed exposition to induce new researchers, not only in Probability and Statistics, but also from applied fields like Engineering