Probabilistic Analysis and Related Topics
Volume 1
- 1st Edition - May 10, 2014
- Editor: A. T. Bharucha-Reid
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 3 6 1 6 - 2
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 6 6 5 - 6
Probabilistic Analysis and Related Topics, Volume 1 focuses on the continuity, differentiability, and integrability of random functions, including functional analysis, operator… Read more
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Request a sales quoteProbabilistic Analysis and Related Topics, Volume 1 focuses on the continuity, differentiability, and integrability of random functions, including functional analysis, operator theory, measure theory, and numerical analysis. The selection first offers information on stochastic partial differential equations in turbulence related problems and estimation and stochastic control for linear infinite-dimensional systems. Discussions focus on deterministic quadratic cost-control problem; partial differential equations in stochastic wave propagation; and theory of stochastic partial differential equations. The text then examines random integrodifferential equations, including small perturbations, existence and uniqueness of solutions, stochastic properties of solution processes, and vibration string. The manuscript ponders on equivalence and singularity of Gaussian measures and applications and stochastic Riemannian geometry. Concerns include semilocal properties, Brownian motion, reproducing kernel Hilbert spaces and Gaussian processes, equivalence and singularity of Gaussian processes, and general problem of equivalence and singularity. The selection is a vital source of information for mathematicians and researchers interested in the general theory of random functions.
List of Contributors
Preface
Stochastic Partial Differential Equations in Turbulence Related Problems
I. Introduction
II. Theory of Stochastic Partial Differential Equations
III. Linear Stochastic Partial Differential Equations in Weak Turbulence
IV. Partial Differential Equations in Stochastic Wave Propagation
V. Stochastic Equations in Turbulent Transport Theory
VI. Markovian Model Equations in Turbulence
References
Estimation and Stochastic Control for Linear Infinite-Dimensional Systems
I. Introduction
II. The Semigroup Description of Linear Autonomous Systems
III. Stochastic Evolution Equations
IV. Deterministic Quadratic Cost-Control Problem
V. State Estimation
VI. The Separation Principle for Stochastic Optimal Control
VII. Extensions
References
Random Integrodifferential Equations
I. Introduction and Preliminaries
II. Existence and Uniqueness of Solution
III. Some Stochastic Properties of Solution Processes
IV. Small Perturbations
V. Vibrating String
References
Equivalence and Singularity of Gaussian Measures and Applications
I. Introduction
II. General Problem of Equivalence and Singularity
III. Reproducing Kernel Hilbert Spaces and Gaussian Processes
IV. Equivalence and Singularity of Gaussian Processes
V. Conditions for Equivalence: Special Cases
VI. Applications
VII. Concluding Remarks
Appendix
References
Stochastic Riemannian Geometry
I. Introduction
II. Brownian Motion
III. Semilocal Properties
IV. Asymptotic Properties, t → 0
V. Asymptotic Properties, t → ∞
VI. Bibliographical Remarks
References
Index
- No. of pages: 250
- Language: English
- Edition: 1
- Published: May 10, 2014
- Imprint: Academic Press
- Paperback ISBN: 9781483236162
- eBook ISBN: 9781483276656
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