Bharucha-Reid Probabilistic Analysis and Related Topics

Volume 3
1. Auflage 2014
ISBN: 978-1-4832-7546-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 270 Seiten, Web PDF

Probabilistic Analysis and Related Topics, Volume 3 focuses on the continuity, integrability, and differentiability of random functions, including operator theory, measure theory, and functional and numerical analysis. The selection first offers information on the qualitative theory of stochastic systems and Langevin equations with multiplicative noise. Discussions focus on phase-space evolution via direct integration, phase-space evolution, linear and nonlinear systems, linearization, and generalizations. The text then ponders on the stability theory of stochastic difference systems and Markov properties for random fields. Topics include Markov property of solutions of stochastic partial differential equations; Markov property for generalized Gaussian random fields; Markov properties for generalized random fields; stochastic stability of nonlinear systems; and linear stochastic systems. The publication examines the method of random contractors and its applications to random nonlinear equations, including integral contractors and applications to random equations; random contractors with random nonlinear majorant functions; and random contractors and application to random nonlinear operator equations. The selection is a valuable reference 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. Qualitative Theory of Stochastic Systems;12
7.1;I. Introduction;13
7.2;II. Scope of the Theory;14
7.3;III. Nonlinear Systems;19
7.4;IV. Linear Systems;53
7.5;V. Linearization;79
7.6;VI. Generalizations;80
7.7;VII. Applications;81
7.8;References;84
8;Chapter 2. Langevin Equations with Multiplicative Noise: Theory and Applications to Physical Processes;92
8.1;I. Introduction;93
8.2;II. Phase-Space Evolution: Cumulant Expansion Technique(Stratonovich);101
8.3;III. Phase-Space Evolution via Direct Integration (Itô and Stratonovich);111
8.4;IV. Examples;118
8.5;References;134
9;Chapter 3. Stability Theory of Stochastic Difference Systems;138
9.1;I. Introduction;138
9.2;II. Linear Stochastic Systems;143
9.3;III. Stochastic Stability of Nonlinear Systems;151
9.4;IV. Directions for Further Research;165
9.5;References;169
10;Chapter 4. Markov Properties for Random Fields;172
10.1;Introduction;172
10.2;I. Conditional Independence and Its Consequences;173
10.3;II. Markov Properties for Multiparameter Processes;175
10.4;III. Markov Property on a Class of Sets;177
10.5;IV. Markov Properties for Generalized Random Fields;181
10.6;V. Quasi-Invariant Measures and the Markov Property;185
10.7;VI. Markov Property for Generalized Gaussian Random Fields;189
10.8;VII. Markov Property for Solutions of Stochastic Partial Differential Equations;197
10.9;Appendix A: Gaussian Processes and Reproducing Kernel Spaces;198
10.10;Appendix B: Generalized Gaussian Random Field;200
10.11;References;203
11;Chapter 5. The Method of Random Contractors and Its Applications to Random Nonlinear Equations;206
11.1;I. Introduction;207
11.2;II. Contractors and Deterministic Nonlinear Operators;208
11.3;III. Preliminary Definitions;211
11.4;IV. Random Contractors and Application to Random Nonlinear Operator Equations;215
11.5;V. Random Contractors with Random Nonlinear Majorant Functions;233
11.6;VI. Random Step-Contractors;242
11.7;VII. Integral Contractors and Applications to Random Equations;248
11.8;References;264
12;Index;268