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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
Qualitative Theory of Stochastic Systems
II. Scope of the Theory
III. Nonlinear Systems
IV. Linear Systems
Langevin Equations with Multiplicative Noise: Theory and Applications to Physical Processes
II. Phase-Space Evolution: Cumulant Expansion Technique (Stratonovich)
III. Phase-Space Evolution via Direct Integration (Itô and Stratonovich)
Stability Theory of Stochastic Difference Systems
II. Linear Stochastic Systems
III. Stochastic Stability of Nonlinear Systems
IV. Directions for Further Research
Markov Properties for Random Fields
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
The Method of Random Contractors and Its Applications to Random Nonlinear Equations
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
- No. of pages:
- © Academic Press 1983
- 28th January 1983
- Academic Press
- eBook ISBN: