Stochastic Analysis And Random Maps In Hilbert Space

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Stochastic Analysis and Random Maps in Hilbert Space

Author : A. A. Dorogovtsev
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110618141
Total Pages : 116 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Stochastic Analysis and Random Maps in Hilbert Space by : A. A. Dorogovtsev

Download or read book Stochastic Analysis and Random Maps in Hilbert Space written by A. A. Dorogovtsev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-01-14 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to stochastic operators in Hilbert space. A number of models in modern probability theory apply the notion of a stochastic operator in explicit or latent form. In this book, objects from the Gaussian case are considered. Therefore, it is useful to consider all random variables and elements as functionals from the Wiener process or its formal derivative, i.e. white noise. The book consists of five chapters. The first chapter is devoted to stochastic calculus and its main goal is to prepare the tools for solving stochastic equations. In the second chapter the structure of stochastic equations, mainly the structure of Gaussian strong linear operators, is studied. In chapter 3 the definition of the action of the stochastic operator on random elements in considered. Chapter 4 deals with the mathematical models in which the notions of stochastic calculus arise and in the final chapter the equation with random operators is considered.

Stochastic Analysis and Random Maps in Hilbert Space

Author : A. A. Dorogovt͡sev
Publisher : VSP
ISBN 13 : 9789067641630
Total Pages : 122 pages
Book Rating : 4.6/5 (416 download)

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Book Synopsis Stochastic Analysis and Random Maps in Hilbert Space by : A. A. Dorogovt͡sev

Download or read book Stochastic Analysis and Random Maps in Hilbert Space written by A. A. Dorogovt͡sev and published by VSP. This book was released on 1994-01-01 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to stochastic operators in Hilbert space. A number of models in modern probability theory apply the notion of a stochastic operator in explicit or latent form. In this book, objects from the Gaussian case are considered. Therefore, it is useful to consider all random variables and elements as functionals from the Wiener process or its formal derivative, i.e. white noise. The book consists of five chapters. The first chapter is devoted to stochastic calculus and its main goal is to prepare the tools for solving stochastic equations. In the second chapter the structure of stochastic equations, mainly the structure of Gaussian strong linear operators, is studied. In chapter 3 the definition of the action of the stochastic operator on random elements in considered. Chapter 4 deals with the mathematical models in which the notions of stochastic calculus arise and in the final chapter the equation with random operators is considered.

Stochastic Processes and Applications

Author : Grigorios A. Pavliotis
Publisher : Springer
ISBN 13 : 1493913239
Total Pages : 345 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Stochastic Processes and Applications by : Grigorios A. Pavliotis

Download or read book Stochastic Processes and Applications written by Grigorios A. Pavliotis and published by Springer. This book was released on 2014-11-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.

Stochastic Finite Elements: A Spectral Approach

Author : Roger G. Ghanem
Publisher : Springer Science & Business Media
ISBN 13 : 1461230942
Total Pages : 217 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Stochastic Finite Elements: A Spectral Approach by : Roger G. Ghanem

Download or read book Stochastic Finite Elements: A Spectral Approach written by Roger G. Ghanem and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph considers engineering systems with random parame ters. Its context, format, and timing are correlated with the intention of accelerating the evolution of the challenging field of Stochastic Finite Elements. The random system parameters are modeled as second order stochastic processes defined by their mean and covari ance functions. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used' to represent these processes in terms of a countable set of un correlated random vari ables. Thus, the problem is cast in a finite dimensional setting. Then, various spectral approximations for the stochastic response of the system are obtained based on different criteria. Implementing the concept of Generalized Inverse as defined by the Neumann Ex pansion, leads to an explicit expression for the response process as a multivariate polynomial functional of a set of un correlated random variables. Alternatively, the solution process is treated as an element in the Hilbert space of random functions, in which a spectral repre sentation in terms of the Polynomial Chaoses is identified. In this context, the solution process is approximated by its projection onto a finite subspace spanned by these polynomials.

The Generic Chaining

Author : Michel Talagrand
Publisher : Springer Science & Business Media
ISBN 13 : 3540274995
Total Pages : 227 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis The Generic Chaining by : Michel Talagrand

Download or read book The Generic Chaining written by Michel Talagrand and published by Springer Science & Business Media. This book was released on 2005-12-08 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental question of characterizing continuity and boundedness of Gaussian processes goes back to Kolmogorov. After contributions by R. Dudley and X. Fernique, it was solved by the author. This book provides an overview of "generic chaining", a completely natural variation on the ideas of Kolmogorov. It takes the reader from the first principles to the edge of current knowledge and to the open problems that remain in this domain.

Hilbert Space Methods in Probability and Statistical Inference

Author : Christopher G. Small
Publisher : John Wiley & Sons
ISBN 13 : 1118165535
Total Pages : 268 pages
Book Rating : 4.1/5 (181 download)

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Book Synopsis Hilbert Space Methods in Probability and Statistical Inference by : Christopher G. Small

Download or read book Hilbert Space Methods in Probability and Statistical Inference written by Christopher G. Small and published by John Wiley & Sons. This book was released on 2011-09-15 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains how Hilbert space techniques cross the boundaries into the foundations of probability and statistics. Focuses on the theory of martingales stochastic integration, interpolation and density estimation. Includes a copious amount of problems and examples.

Introduction to Stochastic Calculus with Applications

Author : Fima C. Klebaner
Publisher : Imperial College Press
ISBN 13 : 1860945554
Total Pages : 431 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis Introduction to Stochastic Calculus with Applications by : Fima C. Klebaner

Download or read book Introduction to Stochastic Calculus with Applications written by Fima C. Klebaner and published by Imperial College Press. This book was released on 2005 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.

Hilbert And Banach Space-valued Stochastic Processes

Author : Yuichiro Kakihara
Publisher : World Scientific
ISBN 13 : 9811211760
Total Pages : 539 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Hilbert And Banach Space-valued Stochastic Processes by : Yuichiro Kakihara

Download or read book Hilbert And Banach Space-valued Stochastic Processes written by Yuichiro Kakihara and published by World Scientific. This book was released on 2021-07-29 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

New Trends in Stochastic Analysis and Related Topics

Author : Huaizhong Zhao
Publisher : World Scientific
ISBN 13 : 9814360910
Total Pages : 458 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis New Trends in Stochastic Analysis and Related Topics by : Huaizhong Zhao

Download or read book New Trends in Stochastic Analysis and Related Topics written by Huaizhong Zhao and published by World Scientific. This book was released on 2012 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc.

Linear Processes in Function Spaces

Author : Denis Bosq
Publisher : Springer Science & Business Media
ISBN 13 : 1461211549
Total Pages : 295 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Linear Processes in Function Spaces by : Denis Bosq

Download or read book Linear Processes in Function Spaces written by Denis Bosq and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main subject of this book is the estimation and forecasting of continuous time processes. It leads to a development of the theory of linear processes in function spaces. Mathematical tools are presented, as well as autoregressive processes in Hilbert and Banach spaces and general linear processes and statistical prediction. Implementation and numerical applications are also covered. The book assumes knowledge of classical probability theory and statistics.

Applied Stochastic Differential Equations

Author : Simo Särkkä
Publisher : Cambridge University Press
ISBN 13 : 1316510085
Total Pages : 327 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä

Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Stochastic Analysis: A Series of Lectures

Author : Robert C. Dalang
Publisher : Birkhäuser
ISBN 13 : 3034809093
Total Pages : 402 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Stochastic Analysis: A Series of Lectures by : Robert C. Dalang

Download or read book Stochastic Analysis: A Series of Lectures written by Robert C. Dalang and published by Birkhäuser. This book was released on 2015-07-28 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or Lévy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential equations with reflection. The articles are based on short courses given at the Centre Interfacultaire Bernoulli of the Ecole Polytechnique Fédérale de Lausanne, Switzerland, from January to June 2012. They offer a valuable resource not only for specialists, but also for other researchers and Ph.D. students in the fields of stochastic analysis and mathematical physics. Contributors: S. Albeverio M. Arnaudon V. Bally V. Barbu H. Bessaih Z. Brzeźniak K. Burdzy A.B. Cruzeiro F. Flandoli A. Kohatsu-Higa S. Mazzucchi C. Mueller J. van Neerven M. Ondreját S. Peszat M. Veraar L. Weis J.-C. Zambrini

Probability Theory and Stochastic Processes with Applications (Second Edition)

Author : Oliver Knill
Publisher : World Scientific Publishing Company
ISBN 13 : 9789813109490
Total Pages : 500 pages
Book Rating : 4.1/5 (94 download)

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Book Synopsis Probability Theory and Stochastic Processes with Applications (Second Edition) by : Oliver Knill

Download or read book Probability Theory and Stochastic Processes with Applications (Second Edition) written by Oliver Knill and published by World Scientific Publishing Company. This book was released on 2017-01-31 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition has a unique approach that provides a broad and wide introduction into the fascinating area of probability theory. It starts on a fast track with the treatment of probability theory and stochastic processes by providing short proofs. The last chapter is unique as it features a wide range of applications in other fields like Vlasov dynamics of fluids, statistics of circular data, singular continuous random variables, Diophantine equations, percolation theory, random Schrödinger operators, spectral graph theory, integral geometry, computer vision, and processes with high risk.Many of these areas are under active investigation and this volume is highly suited for ambitious undergraduate students, graduate students and researchers.

Industrial Revolution 4.0

Author : Stanisław Mazur
Publisher : Taylor & Francis
ISBN 13 : 1000646122
Total Pages : 239 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis Industrial Revolution 4.0 by : Stanisław Mazur

Download or read book Industrial Revolution 4.0 written by Stanisław Mazur and published by Taylor & Francis. This book was released on 2022-09-28 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: The radical transformations to which the economy and society have been subjected for decades have gained momentum in recent years, not least because of the coronavirus pandemic, the consequences of which are yet to be fully understood. As a result, certain economic models and business practices are becoming less sustainable. One of the reasons for this is the rapid advance of Revolution 4.0. The issues raised in this book are central to understanding the theoretical and practical aspects of the Fourth Industrial Revolution and its overwhelming impact on emerging socio-economic relations. The book addresses the future and flexibility of the labour market in the era of digital transformation; issues related to the emergence of new patterns of production and the distribution of public services. It examines the impact of Revolution 4.0 on the global business services sector and business project management models, in times of increasing complexity. The book covers a broad spectrum of concerns associated with Industry 4.0, such as social, economic, technological, and environmental, making it a comprehensive resource offering state-of-the-art knowledge. Further, it includes a discussion on the perspectives for the development of Revolution 4.0 in the context of the post-pandemic world. This book skillfully combines theoretical considerations with practical applications, offering a valuable, engaging and accessible resource for researchers, scholars, students, policymakers, public decision-makers, and businesspeople alike.

Many Valued Topology and its Applications

Author : Ulrich Höhle
Publisher : Springer Science & Business Media
ISBN 13 : 146151617X
Total Pages : 377 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Many Valued Topology and its Applications by : Ulrich Höhle

Download or read book Many Valued Topology and its Applications written by Ulrich Höhle and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 20th Century brought the rise of General Topology. It arose from the effort to establish a solid base for Analysis and it is intimately related to the success of set theory. Many Valued Topology and Its Applications seeks to extend the field by taking the monadic axioms of general topology seriously and continuing the theory of topological spaces as topological space objects within an almost completely ordered monad in a given base category C. The richness of this theory is shown by the fundamental fact that the category of topological space objects in a complete and cocomplete (epi, extremal mono)-category C is topological over C in the sense of J. Adamek, H. Herrlich, and G.E. Strecker. Moreover, a careful, categorical study of the most important topological notions and concepts is given - e.g., density, closedness of extremal subobjects, Hausdorff's separation axiom, regularity, and compactness. An interpretation of these structures, not only by the ordinary filter monad, but also by many valued filter monads, underlines the richness of the explained theory and gives rise to new concrete concepts of topological spaces - so-called many valued topological spaces. Hence, many valued topological spaces play a significant role in various fields of mathematics - e.g., in the theory of locales, convergence spaces, stochastic processes, and smooth Borel probability measures. In its first part, the book develops the necessary categorical basis for general topology. In the second part, the previously given categorical concepts are applied to monadic settings determined by many valued filter monads. The third part comprises various applications of many valued topologies to probability theory and statistics as well as to non-classical model theory. These applications illustrate the significance of many valued topology for further research work in these important fields.

Functional Analysis for Probability and Stochastic Processes

Author : Adam Bobrowski
Publisher : Cambridge University Press
ISBN 13 : 9780521831666
Total Pages : 416 pages
Book Rating : 4.8/5 (316 download)

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Book Synopsis Functional Analysis for Probability and Stochastic Processes by : Adam Bobrowski

Download or read book Functional Analysis for Probability and Stochastic Processes written by Adam Bobrowski and published by Cambridge University Press. This book was released on 2005-08-11 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents selected areas of functional analysis that can facilitate an understanding of ideas in probability and stochastic processes. Topics covered include basic Hilbert and Banach spaces, weak topologies and Banach algebras, and the theory ofsemigroups of bounded linear operators.

Quantum Stochastic Thermodynamics

Author : Philipp Strasberg
Publisher : Oxford University Press
ISBN 13 : 0192895583
Total Pages : 337 pages
Book Rating : 4.1/5 (928 download)

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Book Synopsis Quantum Stochastic Thermodynamics by : Philipp Strasberg

Download or read book Quantum Stochastic Thermodynamics written by Philipp Strasberg and published by Oxford University Press. This book was released on 2022 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of thermodynamics has been one of the bedrocks of 19th-century physics, and thermodynamic problems have inspired Planck's quantum hypothesis. One hundred years later, in an era where we design increasingly sophisticated nanotechnologies, researchers in quantum physics have been 'returning to their roots', attempting to reconcile modern nanoscale devices with the theory of thermodynamics. This textbook explains how it is possible to unify the two opposite pictures of microscopic quantum physics and macroscopic thermodynamics in one consistent framework, proving that the ancient theory of thermodynamics still offers many remarkable insights into present-day problems. This textbook focuses on the microscopic derivation and understanding of key principles and concepts and their interrelation. The topics covered in this book include (quantum) stochastic processes, (quantum) master equations, local detailed balance, classical stochastic thermodynamics, (quantum) fluctuation theorems, strong coupling and non-Markovian effects, thermodynamic uncertainty relations, operational approaches, Maxwell's demon, and time-reversal symmetry, among other topics. The textbook also explores several practical applications of the theory in more detail, including single-molecule pulling experiments, quantum transport and thermoelectric effects in quantum dots, the micromaser, and related setups in quantum optics. The aim of this book is to inspire readers to investigate a plethora of modern nanoscale devices from a thermodynamic point of view, allowing them to address their dissipation, efficiency, reliability, and power based on a conceptually clear understanding about the microscopic origin of heat, entropy, and the second law. The book is accessible to graduate students, post-docs, and lecturers, but will also be of interest to all researchers striving for a deeper understanding of the laws of thermodynamics beyond their traditional realm of applicability.