Bharucha-Reid Probabilistic Analysis and Related Topics

Volume 1
1. Auflage 2014
ISBN: 978-1-4832-7665-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 250 Seiten, Web PDF

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.

Autoren/Hrsg.

Bharucha-Reid, A. T.

Inhaltsverzeichnis

1;Front Cover;1
2;Probabilistic Analysis and Related Topics;4
3;Copyright Page;5
4;Table of Contents;6
5;List of Contributors;8
6;Preface;10
7;Chapter 1. Stochastic Partial Differential Equations
in Turbulence Related Problems;12
7.1;I. Introduction;13
7.2;II. Theory of Stochastic Partial Differential Equations;14
7.3;III. Linear Stochastic Partial Differential Equations in Weak Turbulence;29
7.4;IV. Partial Differential Equations in Stochastic Wave Propagation;33
7.5;V. Stochastic Equations in Turbulent Transport Theory;39
7.6;VI. Markovian Model Equations in Turbulence;44
7.7;ACKNOWLEDGMENTS;51
7.8;REFERENCES;51
8;Chapter 2. Estimation and Stochastic Control
for Linear Infinite-Dimensional Systems;56
8.1;I. Introduction;56
8.2;II. The Semigroup Description of Linear Autonomous Systems;57
8.3;III. Stochastic Evolution Equations;62
8.4;IV. Deterministic Quadratic Cost-Control Problem;71
8.5;V. State Estimation;75
8.6;VI. The Separation Principle for Stochastic Optimal Control;80
8.7;VII. Extensions;84
8.8;REFERENCES;95
9;Chapter 3. Random Integrodìfferentìal Equations;98
9.1;I. Introduction and Preliminaries;98
9.2;II. Existence and Uniqueness of Solutions;114
9.3;III. Some Stochastic Properties of Solution Processes;137
9.4;IV. Small Perturbations;159
9.5;V. Vibrating String;168
9.6;REFERENCES;176
10;Chapter 4. Equivalence and Singularity of
Gaussian Measures and Applications;180
10.1;I. Introduction;180
10.2;II. General Problem of Equivalence and Singularity;182
10.3;III. Reproducing Kernel Hilbert Spaces and Gaussian Processes;186
10.4;IV. Equivalence and Singularity of Gaussian Processes;191
10.5;V. Conditions for Equivalence: Special Cases;196
10.6;VI. Applications;200
10.7;VII. Concluding Remarks;205
10.8;Appendix;205
10.9;ACKNOWLEDGMENTS;206
10.10;REFERENCES;206
11;Chapter 5. Stochastic Riemannian Geometry;210
11.1;I. Introduction;210
11.2;II. Brownian Motion;212
11.3;III. Semilocal Properties;221
11.4;IV. Asymptotic Properties, t
. 0;227
11.5;V. Asymptotic Properties, t .
8;232
11.6;VI. Bibliographical Remarks;245
11.7;REFERENCES;245
12;Index;248