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The Resource Almost Periodic Stochastic Processes, by Paul H. Bezandry, Toka Diagana, (electronic resource)
Almost Periodic Stochastic Processes, by Paul H. Bezandry, Toka Diagana, (electronic resource)
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The item Almost Periodic Stochastic Processes, by Paul H. Bezandry, Toka Diagana, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Almost Periodic Stochastic Processes, by Paul H. Bezandry, Toka Diagana, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 Almost Periodic Stochastic Processes is among the few published books that is entirely devoted to almost periodic stochastic processes and their applications. The topics treated range from existence, uniqueness, boundedness, and stability of solutions, to stochastic difference and differential equations. Motivated by the studies of the natural fluctuations in nature, this work aims to lay the foundations for a theory on almost periodic stochastic processes and their applications. This book is divided in to eight chapters and offers useful bibliographical notes at the end of each chapter. Highlights of this monograph include the introduction of the concept of pth mean almost periodicity for stochastic processes and applications to various equations. The book offers some original results on the boundedness, stability, and existence of pth mean almost periodic solutions to (non)autonomous first and/or second order stochastic differential equations, stochastic partial differential equations, stochastic functional differential equations with delay, and stochastic difference equations. Various illustrative examples are also discussed throughout the book. The results provided in the book will be of particular use to those conducting research in the field of stochastic processing including engineers, economists, and statisticians with backgrounds in functional analysis and stochastic analysis. Advanced graduate students with backgrounds in real analysis, measure theory, and basic probability, may also find the material in this book quite useful and engaging
 Language

 eng
 eng
 Edition
 1st ed. 2011.
 Extent
 1 online resource (246 p.)
 Note
 Description based upon print version of record
 Contents

 Almost Periodic Stochastic Processes; Acknowledgments; Preface; Contents; Chapter 1 Banach and Hilbert Spaces; 1.1 Banach Spaces; 1.1.1 Introduction; 1.1.2 Normed Vector Spaces; 1.1.3 Examples of Banach Spaces; 1.1.4 Hölder and Lipschitz Spaces; 1.2 Hilbert Spaces; 1.2.1 Basic Definitions; 1.2.2 Orthogonality; 1.2.3 Projections; 1.3 Bibliographical Notes; Chapter 2 Bounded and Unbounded Linear Operators; 2.1 Introduction; 2.2 Linear Operators; 2.2.1 Bounded Operators; 2.2.1.1 Adjoint For Bounded Operators; 2.2.1.2 The Inverse Operator; 2.2.1.3 Compact Operators
 2.2.1.4 HilbertSchmidt Operators2.2.2 Unbounded Linear Operators; 2.2.3 Examples of Unbounded Operators; 2.2.3.1 Closed and Closable Linear Operators; 2.2.3.2 Spectral Theory for Unbounded Linear Operators; 2.2.3.3 Symmetric and SelfAdjoint Linear Operators; 2.3 Sectorial Linear Operators; 2.3.1 Basic Definitions; 2.3.2 Examples of Sectorial Operators; 2.4 Semigroups of Linear Operators; 2.4.1 Basic Definitions; 2.4.2 Basic Properties of Semigroups; 2.4.3 Analytic Semigroups; 2.5 Intermediate Spaces; 2.5.1 Fractional Powers of Sectorial Operators; 2.5.2 The Spaces DA(α, p) and DA(α)
 2.5.3 Hyperbolic Semigroups2.6 Evolution Families and Their Properties; 2.6.1 Evolution Families; 2.6.2 Estimates for U(t, s); 2.7 Bibliographical Notes; Chapter 3 An Introduction to Stochastic Differential Equations; 3.1 Fundamentals of Probability; 3.1.1 Probability and Random Variables; 3.1.2 Sequence of Events; 3.1.3 Convergence of Random Variables; 3.1.3.1 Convergence in Distribution; 3.1.3.2 Convergence in Probability; 3.1.3.3 Almost Sure Convergence; 3.1.3.4 LpConvergence; 3.1.4 Conditional Expectation; 3.2 Stochastic Processes; 3.2.1 Continuity; 3.2.2 Separability and Measurability
 3.2.3 Stopping Times3.2.4 Gaussian Processes; 3.2.5 Martingales; 3.3 Stochastic Integrals in One Dimension; 3.3.1 Motivation; 3.3.2 Itô Integrals; 3.3.3 Itô Integrals with Stopping Time; 3.3.4 Itô Formula; 3.3.5 Diffusion Process; 3.4 Wiener Process and Stochastic Integrals in a Hilbert Space; 3.4.1 Wiener Process in a Separable Hilbert Space; 3.4.2 Stochastic Integrals in a Hilbert Space; 3.4.3 Stochastic Convolution Integrals; 3.5 Existence of Solutions of Stochastic Differential Equations in a Hilbert Space; 3.5.1 Existence and Uniqueness; 3.5.2 L2Bounded Solutions
 3.5.3 Stochastic Delay Differential Equation and Exponential Stability3.6 Bibliographical Notes; Chapter 4 pth Mean Almost Periodic Random Functions; 4.1 Almost Periodic Functions; 4.1.1 Introduction; 4.1.2 Basic Definitions; 4.1.3 Properties of Almost Periodic Functions; 4.2 pth Mean Almost Periodic Processes; 4.2.1 Composition of pth Mean Almost Periodic Processes; 4.3 Bibliographical Notes; Chapter 5 Existence Results for Some Stochastic Differential Equations; 5.1 The Autonomous Case; 5.2 The Nonautonomous Case; 5.2.1 Introduction; 5.2.2 Existence of pth Mean Almost Periodic Solutions
 5.2.3 Example
 Isbn
 9781441994769
 Label
 Almost Periodic Stochastic Processes
 Title
 Almost Periodic Stochastic Processes
 Statement of responsibility
 by Paul H. Bezandry, Toka Diagana
 Subject

 Integral Equations
 Differential Equations
 Operator theory
 Functional analysis
 Partial Differential Equations
 Distribution (Probability theory
 Functional Analysis
 Ordinary Differential Equations
 Integral equations
 Differential equations, partial
 Probability Theory and Stochastic Processes
 Operator Theory
 Language

 eng
 eng
 Summary
 Almost Periodic Stochastic Processes is among the few published books that is entirely devoted to almost periodic stochastic processes and their applications. The topics treated range from existence, uniqueness, boundedness, and stability of solutions, to stochastic difference and differential equations. Motivated by the studies of the natural fluctuations in nature, this work aims to lay the foundations for a theory on almost periodic stochastic processes and their applications. This book is divided in to eight chapters and offers useful bibliographical notes at the end of each chapter. Highlights of this monograph include the introduction of the concept of pth mean almost periodicity for stochastic processes and applications to various equations. The book offers some original results on the boundedness, stability, and existence of pth mean almost periodic solutions to (non)autonomous first and/or second order stochastic differential equations, stochastic partial differential equations, stochastic functional differential equations with delay, and stochastic difference equations. Various illustrative examples are also discussed throughout the book. The results provided in the book will be of particular use to those conducting research in the field of stochastic processing including engineers, economists, and statisticians with backgrounds in functional analysis and stochastic analysis. Advanced graduate students with backgrounds in real analysis, measure theory, and basic probability, may also find the material in this book quite useful and engaging
 http://library.link/vocab/creatorName
 Bezandry, Paul H
 Dewey number
 519.23
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut

 8Yd5hMzSw
 dHvP0rTS8gI
 Language note
 English
 LC call number
 QA372
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Diagana, Toka.
 http://library.link/vocab/subjectName

 Differential Equations
 Distribution (Probability theory
 Differential equations, partial
 Functional analysis
 Operator theory
 Integral equations
 Ordinary Differential Equations
 Probability Theory and Stochastic Processes
 Partial Differential Equations
 Functional Analysis
 Operator Theory
 Integral Equations
 Label
 Almost Periodic Stochastic Processes, by Paul H. Bezandry, Toka Diagana, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents

 Almost Periodic Stochastic Processes; Acknowledgments; Preface; Contents; Chapter 1 Banach and Hilbert Spaces; 1.1 Banach Spaces; 1.1.1 Introduction; 1.1.2 Normed Vector Spaces; 1.1.3 Examples of Banach Spaces; 1.1.4 Hölder and Lipschitz Spaces; 1.2 Hilbert Spaces; 1.2.1 Basic Definitions; 1.2.2 Orthogonality; 1.2.3 Projections; 1.3 Bibliographical Notes; Chapter 2 Bounded and Unbounded Linear Operators; 2.1 Introduction; 2.2 Linear Operators; 2.2.1 Bounded Operators; 2.2.1.1 Adjoint For Bounded Operators; 2.2.1.2 The Inverse Operator; 2.2.1.3 Compact Operators
 2.2.1.4 HilbertSchmidt Operators2.2.2 Unbounded Linear Operators; 2.2.3 Examples of Unbounded Operators; 2.2.3.1 Closed and Closable Linear Operators; 2.2.3.2 Spectral Theory for Unbounded Linear Operators; 2.2.3.3 Symmetric and SelfAdjoint Linear Operators; 2.3 Sectorial Linear Operators; 2.3.1 Basic Definitions; 2.3.2 Examples of Sectorial Operators; 2.4 Semigroups of Linear Operators; 2.4.1 Basic Definitions; 2.4.2 Basic Properties of Semigroups; 2.4.3 Analytic Semigroups; 2.5 Intermediate Spaces; 2.5.1 Fractional Powers of Sectorial Operators; 2.5.2 The Spaces DA(α, p) and DA(α)
 2.5.3 Hyperbolic Semigroups2.6 Evolution Families and Their Properties; 2.6.1 Evolution Families; 2.6.2 Estimates for U(t, s); 2.7 Bibliographical Notes; Chapter 3 An Introduction to Stochastic Differential Equations; 3.1 Fundamentals of Probability; 3.1.1 Probability and Random Variables; 3.1.2 Sequence of Events; 3.1.3 Convergence of Random Variables; 3.1.3.1 Convergence in Distribution; 3.1.3.2 Convergence in Probability; 3.1.3.3 Almost Sure Convergence; 3.1.3.4 LpConvergence; 3.1.4 Conditional Expectation; 3.2 Stochastic Processes; 3.2.1 Continuity; 3.2.2 Separability and Measurability
 3.2.3 Stopping Times3.2.4 Gaussian Processes; 3.2.5 Martingales; 3.3 Stochastic Integrals in One Dimension; 3.3.1 Motivation; 3.3.2 Itô Integrals; 3.3.3 Itô Integrals with Stopping Time; 3.3.4 Itô Formula; 3.3.5 Diffusion Process; 3.4 Wiener Process and Stochastic Integrals in a Hilbert Space; 3.4.1 Wiener Process in a Separable Hilbert Space; 3.4.2 Stochastic Integrals in a Hilbert Space; 3.4.3 Stochastic Convolution Integrals; 3.5 Existence of Solutions of Stochastic Differential Equations in a Hilbert Space; 3.5.1 Existence and Uniqueness; 3.5.2 L2Bounded Solutions
 3.5.3 Stochastic Delay Differential Equation and Exponential Stability3.6 Bibliographical Notes; Chapter 4 pth Mean Almost Periodic Random Functions; 4.1 Almost Periodic Functions; 4.1.1 Introduction; 4.1.2 Basic Definitions; 4.1.3 Properties of Almost Periodic Functions; 4.2 pth Mean Almost Periodic Processes; 4.2.1 Composition of pth Mean Almost Periodic Processes; 4.3 Bibliographical Notes; Chapter 5 Existence Results for Some Stochastic Differential Equations; 5.1 The Autonomous Case; 5.2 The Nonautonomous Case; 5.2.1 Introduction; 5.2.2 Existence of pth Mean Almost Periodic Solutions
 5.2.3 Example
 Dimensions
 unknown
 Edition
 1st ed. 2011.
 Extent
 1 online resource (246 p.)
 Form of item
 online
 Isbn
 9781441994769
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9781441994769
 Specific material designation
 remote
 System control number

 (CKB)2670000000082569
 (EBL)763349
 (OCoLC)728101791
 (SSID)ssj0000508377
 (PQKBManifestationID)11339994
 (PQKBTitleCode)TC0000508377
 (PQKBWorkID)10554656
 (PQKB)11520808
 (DEHe213)9781441994769
 (MiAaPQ)EBC763349
 (EXLCZ)992670000000082569
 Label
 Almost Periodic Stochastic Processes, by Paul H. Bezandry, Toka Diagana, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Content category
 text
 Content type code
 txt
 Contents

 Almost Periodic Stochastic Processes; Acknowledgments; Preface; Contents; Chapter 1 Banach and Hilbert Spaces; 1.1 Banach Spaces; 1.1.1 Introduction; 1.1.2 Normed Vector Spaces; 1.1.3 Examples of Banach Spaces; 1.1.4 Hölder and Lipschitz Spaces; 1.2 Hilbert Spaces; 1.2.1 Basic Definitions; 1.2.2 Orthogonality; 1.2.3 Projections; 1.3 Bibliographical Notes; Chapter 2 Bounded and Unbounded Linear Operators; 2.1 Introduction; 2.2 Linear Operators; 2.2.1 Bounded Operators; 2.2.1.1 Adjoint For Bounded Operators; 2.2.1.2 The Inverse Operator; 2.2.1.3 Compact Operators
 2.2.1.4 HilbertSchmidt Operators2.2.2 Unbounded Linear Operators; 2.2.3 Examples of Unbounded Operators; 2.2.3.1 Closed and Closable Linear Operators; 2.2.3.2 Spectral Theory for Unbounded Linear Operators; 2.2.3.3 Symmetric and SelfAdjoint Linear Operators; 2.3 Sectorial Linear Operators; 2.3.1 Basic Definitions; 2.3.2 Examples of Sectorial Operators; 2.4 Semigroups of Linear Operators; 2.4.1 Basic Definitions; 2.4.2 Basic Properties of Semigroups; 2.4.3 Analytic Semigroups; 2.5 Intermediate Spaces; 2.5.1 Fractional Powers of Sectorial Operators; 2.5.2 The Spaces DA(α, p) and DA(α)
 2.5.3 Hyperbolic Semigroups2.6 Evolution Families and Their Properties; 2.6.1 Evolution Families; 2.6.2 Estimates for U(t, s); 2.7 Bibliographical Notes; Chapter 3 An Introduction to Stochastic Differential Equations; 3.1 Fundamentals of Probability; 3.1.1 Probability and Random Variables; 3.1.2 Sequence of Events; 3.1.3 Convergence of Random Variables; 3.1.3.1 Convergence in Distribution; 3.1.3.2 Convergence in Probability; 3.1.3.3 Almost Sure Convergence; 3.1.3.4 LpConvergence; 3.1.4 Conditional Expectation; 3.2 Stochastic Processes; 3.2.1 Continuity; 3.2.2 Separability and Measurability
 3.2.3 Stopping Times3.2.4 Gaussian Processes; 3.2.5 Martingales; 3.3 Stochastic Integrals in One Dimension; 3.3.1 Motivation; 3.3.2 Itô Integrals; 3.3.3 Itô Integrals with Stopping Time; 3.3.4 Itô Formula; 3.3.5 Diffusion Process; 3.4 Wiener Process and Stochastic Integrals in a Hilbert Space; 3.4.1 Wiener Process in a Separable Hilbert Space; 3.4.2 Stochastic Integrals in a Hilbert Space; 3.4.3 Stochastic Convolution Integrals; 3.5 Existence of Solutions of Stochastic Differential Equations in a Hilbert Space; 3.5.1 Existence and Uniqueness; 3.5.2 L2Bounded Solutions
 3.5.3 Stochastic Delay Differential Equation and Exponential Stability3.6 Bibliographical Notes; Chapter 4 pth Mean Almost Periodic Random Functions; 4.1 Almost Periodic Functions; 4.1.1 Introduction; 4.1.2 Basic Definitions; 4.1.3 Properties of Almost Periodic Functions; 4.2 pth Mean Almost Periodic Processes; 4.2.1 Composition of pth Mean Almost Periodic Processes; 4.3 Bibliographical Notes; Chapter 5 Existence Results for Some Stochastic Differential Equations; 5.1 The Autonomous Case; 5.2 The Nonautonomous Case; 5.2.1 Introduction; 5.2.2 Existence of pth Mean Almost Periodic Solutions
 5.2.3 Example
 Dimensions
 unknown
 Edition
 1st ed. 2011.
 Extent
 1 online resource (246 p.)
 Form of item
 online
 Isbn
 9781441994769
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9781441994769
 Specific material designation
 remote
 System control number

 (CKB)2670000000082569
 (EBL)763349
 (OCoLC)728101791
 (SSID)ssj0000508377
 (PQKBManifestationID)11339994
 (PQKBTitleCode)TC0000508377
 (PQKBWorkID)10554656
 (PQKB)11520808
 (DEHe213)9781441994769
 (MiAaPQ)EBC763349
 (EXLCZ)992670000000082569
Subject
 Differential Equations
 Differential equations, partial
 Distribution (Probability theory
 Functional Analysis
 Functional analysis
 Integral Equations
 Integral equations
 Operator Theory
 Operator theory
 Ordinary Differential Equations
 Partial Differential Equations
 Probability Theory and Stochastic Processes
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