This extraordinary compilation is an expansion of the recent American Mathematical Society Special Session celebrating M. M. Rao's distinguished career and includes most of the presented papers as well as ancillary contributions from session invitees. This book shows the effectiveness of abstract analysis for solving fundamental problems of stochastic theory, specifically the use of functional analytic methods for elucidating stochastic processes, as made manifest in M. M. Rao's prolific research achievements. Featuring a biography of M. M. Rao, a complete bibliography of his published works, and meditations from former students, the book includes contributions from over 30 notable researchers.
The book is devoted to the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. The spaces can be Banach or Frechet types. Special attention is given to Bochner's boundedness principle and Grothendieck's representation unifying and simplyfying stochastic integrations. Several stationary aspects, extensions and random currents as well as related multilinear forms are analyzed, whilst numerous new procedures and results are included, and many research areas are opened up which also display the geometric aspects in multi dimensions.
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.
Deals with the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. This book analyzes several stationary aspects and related processes.
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.