Hilbert And Banach Space Valued Stochastic Processes
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Hilbert And Banach Space Valued Stochastic Processes
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Author : Yuichiro Kakihara
language : en
Publisher: World Scientific
Release Date : 2021-07-29
Hilbert And Banach Space Valued Stochastic Processes written by Yuichiro Kakihara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-29 with Mathematics categories.
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.
Hilbert And Banach Space Valued Stochastic Processes
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Author : Yūichirō Kakihara
language : en
Publisher:
Release Date : 2021
Hilbert And Banach Space Valued Stochastic Processes written by Yūichirō Kakihara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Banach spaces categories.
"Functional analysis methods are used on stochastic processes. Structural analysis of nonstationary and stationary processes are also included. This book is in the intersection of probability theory and analysis"--
Probability In Banach Spaces
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Author : Michel Ledoux
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Probability In Banach Spaces written by Michel Ledoux and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.
Stochastic Processes And Functional Analysis
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Author : Randall J. Swift
language : en
Publisher: American Mathematical Society
Release Date : 2021-11-22
Stochastic Processes And Functional Analysis written by Randall J. Swift and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-22 with Mathematics categories.
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.
Stochastic Processes Physics And Geometry New Interplays I
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Author : Sergio Albeverio
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Stochastic Processes Physics And Geometry New Interplays I written by Sergio Albeverio and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
A selection of 21 contributions from invited speakers treat advanced topics at the interface between mathematics and physics. Most are high-level research papers, but some overview their topics, among which are growth and saturation in random media, the maximal dissipativity of the Dirichlet operator corresponding to the Burgers equation, the square of the self-intersection local time of Brownian motion, the spectral theory of sparse potentials, and diffusions on simple configuration spaces. Additional short contributions pay tribute to Swiss-born physicist Albeverio. A second volume presents selected volunteer papers. There is no index. Annotation copyrighted by Book News, Inc., Portland, OR
Martingales In Banach Spaces
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Author : Gilles Pisier
language : en
Publisher: Cambridge University Press
Release Date : 2016-06-06
Martingales In Banach Spaces written by Gilles Pisier and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-06 with Mathematics categories.
This book focuses on applications of martingales to the geometry of Banach spaces, and is accessible to graduate students.
Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics
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Author : Wilfried Grecksch
language : en
Publisher: World Scientific
Release Date : 2020-04-22
Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics written by Wilfried Grecksch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-22 with Science categories.
This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
Existence Theory For Generalized Newtonian Fluids
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Author : Dominic Breit
language : en
Publisher: Academic Press
Release Date : 2017-03-22
Existence Theory For Generalized Newtonian Fluids written by Dominic Breit and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-22 with Mathematics categories.
Existence Theory for Generalized Newtonian Fluids provides a rigorous mathematical treatment of the existence of weak solutions to generalized Navier-Stokes equations modeling Non-Newtonian fluid flows. The book presents classical results, developments over the last 50 years of research, and recent results with proofs. - Provides the state-of-the-art of the mathematical theory of Generalized Newtonian fluids - Combines elliptic, parabolic and stochastic problems within existence theory under one umbrella - Focuses on the construction of the solenoidal Lipschitz truncation, thus enabling readers to apply it to mathematical research - Approaches stochastic PDEs with a perspective uniquely suitable for analysis, providing an introduction to Galerkin method for SPDEs and tools for compactness
Multidimensional Second Order Stochastic Processes
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Author : Yichir Kakihara
language : en
Publisher: World Scientific
Release Date : 1997
Multidimensional Second Order Stochastic Processes written by Yichir Kakihara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
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.
Taylor Approximations For Stochastic Partial Differential Equations
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Author : Arnulf Jentzen
language : en
Publisher: SIAM
Release Date : 2011-01-01
Taylor Approximations For Stochastic Partial Differential Equations written by Arnulf Jentzen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.
This book presents a systematic theory of Taylor expansions of evolutionary-type stochastic partial differential equations (SPDEs). The authors show how Taylor expansions can be used to derive higher order numerical methods for SPDEs, with a focus on pathwise and strong convergence. In the case of multiplicative noise, the driving noise process is assumed to be a cylindrical Wiener process, while in the case of additive noise the SPDE is assumed to be driven by an arbitrary stochastic process with Hl̲der continuous sample paths. Recent developments on numerical methods for random and stochastic ordinary differential equations are also included since these are relevant for solving spatially discretised SPDEs as well as of interest in their own right. The authors include the proof of an existence and uniqueness theorem under general assumptions on the coefficients as well as regularity estimates in an appendix.