Random Differential Inequalities
Published on 14. May 2014
225 pages
978-0-08-095658-9 (ISBN)
Description
Random Differential Inequalities
More details
Series
Language
English
Place of publication
San Diego
United States
ISBN-13
978-0-08-095658-9 (9780080956589)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
G. S. Ladde | V. Lakshmikantham
Random Differential Inequalities
Book
01/1980
Academic Press
€61.29
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Content
- Front Cover
- Random Differential Inqualities
- Copyright Page
- Contents
- Preface
- Notations and Abbreviations
- CHAPTER 1. Preliminary Analysis
- 1.0 Introduction
- 1.1 Events and Probability Measure
- 1.2 Random Variables, Distribution Functions, and Expectations
- 1.3 Convergence of Random Sequences
- 1.4 Conditional Probabilities and Expectations
- 1.5 Random Processes
- 1.6 Separability of Random Processes
- 1.7 Deterministic Comparison Theorems
- Notes
- CHAPTER 2. Sample Calculus Approach
- 2.0 Introduction
- 2.1 Sample Calculus
- 2.2 Existence and Continuation
- 2.3 Random Differential Inequalities
- 2.4 Maximal and Minimal Solutions
- 2.5 Random Comparison Principle
- 2.6 Uniqueness and Continuous Dependence
- 2.7 The Method of Variation of Parameters
- 2.8 Random Lyapunov Functions
- 2.9 Scope of Comparison Principle
- 2.10 Stability Concepts
- 2.11 Stability in Probability
- 2.12 Stability with Probability One
- 2.13 Stability in the pth Mean
- Notes
- CHAPTER 3. Lp-calculus Approach
- 3.0 Introduction
- 3.1 Lp-Calculus
- 3.2 Interrelationships between Sample and LP-Solutions
- 3.3 Existence and Uniqueness
- 3.4 Continuous Dependence
- 3.5 Comparison Theorems
- 3.6 Stability Criteria
- Notes
- CHAPTER 4. Itô-Doob Calculus Approach
- 4.0 Introduction
- 4.1 Itô's Calculus
- 4.2 Existence and Uniqueness
- 4.3 Continuous Dependence
- 4.4 The Method of Variation of Parameters
- 4.5 Stochastic Differential Inequalities
- 4.6 Maximal and Minimal Solutions
- 4.7 Comparison Theorems
- 4.8 Lyapunov-Like Functions
- 4.9 Stability in Probability
- 4.10 Stability in the pth Mean
- 4.11 Stability with Probability One
- Notes
- Appendix
- A.0. Introduction
- A.1 Moments of Random Functions
- A.2 Spectral Representations of Covariance and Correlation Functions
- A.3 Some Properties of Gaussian Processes
- A.4 Brownian Motion
- A.5 Martingales
- A.6 Metrically Transitive Processes
- A.7 Markov Processes
- A.8 Closed Graph Theorem
- Notes
- References
- Index
