Probabilistic Analysis and Related Topics (eBook)

Volume 1

A. T. Bharucha-Reid (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
250 Seiten
Elsevier Science (Verlag)
978-1-4832-7665-6 (ISBN)

Infos

Probabilistic Analysis and Related Topics, Volume 1 focuses on the continuity, differentiability, and integrability of random functions, including functional analysis, operator theory, measure theory, and numerical analysis. The selection first offers information on stochastic partial differential equations in turbulence related problems and estimation and stochastic control for linear infinite-dimensional systems. Discussions focus on deterministic quadratic cost-control problem; partial differential equations in stochastic wave propagation; and theory of stochastic partial differential equations. The text then examines random integrodifferential equations, including small perturbations, existence and uniqueness of solutions, stochastic properties of solution processes, and vibration string. The manuscript ponders on equivalence and singularity of Gaussian measures and applications and stochastic Riemannian geometry. Concerns include semilocal properties, Brownian motion, reproducing kernel Hilbert spaces and Gaussian processes, equivalence and singularity of Gaussian processes, and general problem of equivalence and singularity. The selection is a vital source of information for mathematicians and researchers interested in the general theory of random functions.

Inhalt

Front Cover 1
Probabilistic Analysis and Related Topics 4
Copyright Page 5
Table of Contents 6
List of Contributors 8
Preface 10
Chapter 1. Stochastic Partial Differential Equations 
12 
I. Introduction 13
II. Theory of Stochastic Partial Differential Equations 14
III. Linear Stochastic Partial Differential Equations in Weak Turbulence 29
IV. Partial Differential Equations in Stochastic Wave Propagation 33
V. Stochastic Equations in Turbulent Transport Theory 39
VI. Markovian Model Equations in Turbulence 44
ACKNOWLEDGMENTS 51
REFERENCES 51
Chapter 2. Estimation and Stochastic Control 
56 
I. Introduction 56
II. The Semigroup Description of Linear Autonomous Systems 57
III. Stochastic Evolution Equations 62
IV. Deterministic Quadratic Cost-Control Problem 71
V. State Estimation 75
VI. The Separation Principle for Stochastic Optimal Control 80
VII. Extensions 84
REFERENCES 95
Chapter 3. Random Integrodìfferentìal Equations 98
I. Introduction and Preliminaries 98
II. Existence and Uniqueness of Solutions 114
III. Some Stochastic Properties of Solution Processes 137
IV. Small Perturbations 159
V. Vibrating String 168
REFERENCES 176
Chapter 4. Equivalence and Singularity of 
180 
I. Introduction 180
II. General Problem of Equivalence and Singularity 182
III. Reproducing Kernel Hilbert Spaces and Gaussian Processes 186
IV. Equivalence and Singularity of Gaussian Processes 191
V. Conditions for Equivalence: Special Cases 196
VI. Applications 200
VII. Concluding Remarks 205
Appendix 205
ACKNOWLEDGMENTS 206
REFERENCES 206
Chapter 5. Stochastic Riemannian Geometry 210
I. Introduction 210
II. Brownian Motion 212
III. Semilocal Properties 221
IV. Asymptotic Properties, t 
227 
V. Asymptotic Properties, t . 
232 
VI. Bibliographical Remarks 245
REFERENCES 245
Index 248

Produkt-Details

• Erscheint lt. Verlag: 10.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Technik
• ISBN-10: 1-4832-7665-1 / 1483276651
• ISBN-13: 978-1-4832-7665-6 / 9781483276656