Probabilistic Analysis and Related Topics

¿List of ContributorsPrefaceStochastic 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 ReferencesEstimation 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 ReferencesRandom 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 ReferencesEquivalence 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 ReferencesStochastic Riemannian Geometry I. Introduction II. Brownian Motion III. Semilocal Properties IV. Asymptotic Properties, t ¿ 0 V. Asymptotic Properties, t ¿ 8 VI. Bibliographical Remarks ReferencesIndex