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| Author | : Christian Houdre |
| Publisher | : |
| Total Pages | : 29 |
| Release | : 1988 |
| Genre | : |
| ISBN | : |
Some new classes of discrete time non-stationary processes, related to the harmonizable and V-bounded classes, are introduced. A few characterizations are obtained which, in turn, unify the V-bounded theory. Our main results depend on a special form of Grothendieck inequality. (JHD).
| Author | : Malempati Madhusudana Rao |
| Publisher | : World Scientific |
| Total Pages | : 341 |
| Release | : 2020-09-21 |
| Genre | : Mathematics |
| ISBN | : 9811213674 |
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.
| Author | : Abolghassem G. Miamee |
| Publisher | : |
| Total Pages | : 52 |
| Release | : 1977 |
| Genre | : Stationary processes |
| ISBN | : |
| Author | : Malempati M. Rao |
| Publisher | : Springer |
| Total Pages | : 685 |
| Release | : 2014-11-14 |
| Genre | : Mathematics |
| ISBN | : 3319121723 |
This is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics. The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.
| Author | : Yichir Kakihara |
| Publisher | : World Scientific |
| Total Pages | : 352 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9789810230005 |
A research-expository treatment of infinite-dimensional nonstationary stochastic processes (or time series) on a locally compact abelian group is provided with this book. Stochastic measures and scalar or operator bimeasures are fully discussed.
| Author | : Randall J. Swift |
| Publisher | : American Mathematical Society |
| Total Pages | : 248 |
| Release | : 2021-11-22 |
| Genre | : Mathematics |
| ISBN | : 1470459825 |
This volume contains the proceedings of the AMS Special Session on Celebrating M. M. Rao's Many Mathematical Contributions as he Turns 90 Years Old, held from November 9–10, 2019, at the University of California, Riverside, California. The articles show the effectiveness of abstract analysis for solving fundamental problems of stochastic theory, specifically the use of functional analytic methods for elucidating stochastic processes and their applications. The volume also includes a biography of M. M. Rao and the list of his publications.
| Author | : Yuichiro Kakihara |
| Publisher | : World Scientific |
| Total Pages | : 539 |
| Release | : 2021-07-29 |
| Genre | : Mathematics |
| ISBN | : 9811211760 |
This is a development of the book entitled Multidimensional Second Order Stochastic Processes. It provides a research expository treatment of infinite-dimensional stationary and nonstationary stochastic processes or time series, based on Hilbert and Banach space-valued second order random variables. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramér and Karhunen classes as well as the stationary class. A new type of the Radon-Nikodým derivative of a Banach space-valued measure is introduced, together with Schauder basic measures, to study uniformly bounded linearly stationary processes.Emphasis is on the use of functional analysis and harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Generalizations are made to consider Banach space-valued stochastic processes to include processes of pth order for p ≥ 1. Readers may find that the covariance kernel is always emphasized and reveals another aspect of stochastic processes.This book is intended not only for probabilists and statisticians, but also for functional analysts and communication engineers.
| Author | : Malempati M. Rao |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 656 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 1475765967 |
The material accumulated and presented in this volume can be ex plained easily. At the start of my graduate studies in the early 1950s, I Grenander's (1950) thesis, and was much attracted to the came across entire subject considered there. I then began preparing for the neces sary mathematics to appreciate and possibly make some contributions to the area. Thus after a decade of learning and some publications on the way, I wanted to write a modest monograph complementing Grenander's fundamental memoir. So I took a sabbatical leave from my teaching position at the Carnegie-Mellon University, encouraged by an Air Force Grant for the purpose, and followed by a couple of years more learning opportunity at the Institute for Advanced Study to complete the project. As I progressed, the plan grew larger needing a substantial background material which was made into an independent initial volume in (1979). In its preface I said: "My intension was to present the following material as the first part of a book treating the In ference Theory of stochastic processes, but the latter account has now receded to a distant future," namely for two more decades! Meanwhile, a much enlarged second edition of that early work has appeared (1995), and now I am able to present the main part of the original plan.
| Author | : D N Shanbhag |
| Publisher | : Gulf Professional Publishing |
| Total Pages | : 990 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9780444500144 |
This volume in the series contains chapters on areas such as pareto processes, branching processes, inference in stochastic processes, Poisson approximation, Levy processes, and iterated random maps and some classes of Markov processes. Other chapters cover random walk and fluctuation theory, a semigroup representation and asymptomatic behavior of certain statistics of the Fisher-Wright-Moran coalescent, continuous-time ARMA processes, record sequence and their applications, stochastic networks with product form equilibrium, and stochastic processes in insurance and finance. Other subjects include renewal theory, stochastic processes in reliability, supports of stochastic processes of multiplicity one, Markov chains, diffusion processes, and Ito's stochastic calculus and its applications. c. Book News Inc.
