UID:
almahu_9947367010102882
Format:
1 online resource (225 p.)
ISBN:
1-282-29008-8
,
9786612290084
,
0-08-095658-0
Series Statement:
Mathematics in science and engineering ; v. 150
Content:
Random differential inequalities
Note:
Description based upon print version of record.
,
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
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2.4 Maximal and Minimal Solutions2.5 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
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CHAPTER 4. Itô-Doob Calculus Approach4.0 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
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A.4 Brownian MotionA.5 Martingales; A.6 Metrically Transitive Processes; A.7 Markov Processes; A.8 Closed Graph Theorem; Notes; References; Index
,
English
Additional Edition:
ISBN 0-12-432750-8
Language:
English
