Stability of Infinite Dimensional Stochastic Differential Equations with Applications (Hardcover)

PrefaceSTOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONSNotations,Definitions and Preliminaries Wiener Processes and Stochastic Integration Definitions and Methods of Stability Notes and Comments STABILITY F LINEAR STOCHASTIC DIFFERENTIAL EQUATIONSStable Semigroups Lyapunov Equations and Stability Uniformly Asymptotic Stability STABILITY F NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONSEquivalence of L p -Stability and Exponential Stability A Coerciv Decay Condition Stability of Semilinear Stochastic Evolution Equations Lyapunov Functions for Strong Solutions Two Applications Further Results on Invariant Measures Stability,Ultimate Boundedness of Mild Solutions and Invariant Measures Decay Rates of Systems Stabilization of Systems by Noise Lyapunov Exponents and StabilizationNotes and CommentsSTABILITY OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONSLinear Deterministic Equations Stability Equivalence and Reduction of Neutral Equations .Decay Criteria of Stochastic Delay Differential Equations Razumikhin Type Stability Theorems Notes and Comments SOME RELATED TOPICS OF STABILITY AND APPLICATIONSParabolic Equations with Boundary and Pointwise Noise Stochastic Stability and Quadratic Control Feedback Stabilization of Stochastic Differential Equations Stochastic Models in Mathematical Physics Stochastic Systems Related to Multi-Species Population Dynamics Notes and Comments Appendix A: The Proof of PropositionAppendix B: Existence and Uniqueness of Strong Solutions of Stochastic Delay Differential EquationsReferencesIndex