Probabilistic Analysis and Related Topics
Volume 3
- 1st Edition - September 23, 2014
- Imprint: Academic Press
- Editor: A. T. Bharucha-Reid
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 3 6 1 8 - 6
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 5 4 6 - 8
Probabilistic Analysis and Related Topics, Volume 3 focuses on the continuity, integrability, and differentiability of random functions, including operator theory, measure theory,… Read more
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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.
List of Contributors
Preface
Qualitative Theory of Stochastic Systems
I. Introduction
II. Scope of the Theory
III. Nonlinear Systems
IV. Linear Systems
V. Linearization
VI. Generalizations
VII. Applications
References
Langevin Equations with Multiplicative Noise: Theory and Applications to Physical Processes
I. Introduction
II. Phase-Space Evolution: Cumulant Expansion Technique (Stratonovich)
III. Phase-Space Evolution via Direct Integration (Itô and Stratonovich)
IV. Examples
References
Stability Theory of Stochastic Difference Systems
I. Introduction
II. Linear Stochastic Systems
III. Stochastic Stability of Nonlinear Systems
IV. Directions for Further Research
References
Markov Properties for Random Fields
Introduction
I. Conditional Independence and Its Consequences
II. Markov Properties for Multiparameter Processes
III. Markov Property on a Class of Sets
IV. Markov Properties for Generalized Random Fields
V. Quasi-Invariant Measures and the Markov Property
VI. Markov Property for Generalized Gaussian Random Fields
VII. Markov Property for Solutions of Stochastic Partial Differential Equations
Appendix A: Gaussian Processes and Reproducing Kernel Spaces
Appendix B: Generalized Gaussian Random Field
References
The Method of Random Contractors and Its Applications to Random Nonlinear Equations
I. Introduction
II. Contractors and Deterministic Nonlinear Operators
III. Preliminary Definitions
IV. Random Contractors and Application to Random Nonlinear Operator Equations
V. Random Contractors with Random Nonlinear Majorant Functions
VI. Random Step-Contractors
VII. Integral Contractors and Applications to Random Equations
References
Index
- Edition: 1
- Published: September 23, 2014
- Imprint: Academic Press
- Language: English
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