Stability of Infinite Dimensional Stochastic Differential Equations with Applications

Stability of Infinite Dimensional Stochastic Differential Equations with Applications

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Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well established, the study of their stability properties has grown rapidly only in the past 20 years, and most results have remained scattered in journals and conference proceedings. This book offers a systematic presentation of the modern theory of the stability of stochastic differential equations in infinite dimensional spaces - particularly Hilbert spaces. The treatment includes a review of basic concepts and investigation of the stability theory of linear and nonlinear stochastic differential equations and stochastic functional differential equations in infinite dimensions. The final chapter explores topics and applications such as stochastic optimal control and feedback stabilization, stochastic reaction-diffusion, Navier-Stokes equations, and stochastic population dynamics. In recent years, this area of study has become the focus of increasing attention, and the relevant literature has expanded greatly. Stability of Infinite Dimensional Stochastic Differential Equations with Applications makes up-to-date material in this important field accessible even to newcomers and lays the foundation for future advances.show more

Product details

  • Hardback | 312 pages
  • 162.6 x 238.8 x 25.4mm | 453.6g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • New.
  • 158488598X
  • 9781584885986

Table of contents

Preface STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS Notations,Definitions and Preliminaries Wiener Processes and Stochastic Integration Definitions and Methods of Stability Notes and Comments STABILITY F LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS Stable Semigroups Lyapunov Equations and Stability Uniformly Asymptotic Stability STABILITY F NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS Equivalence 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 Stabilization Notes and Comments STABILITY OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS Linear 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 APPLICATIONS Parabolic 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 Proposition Appendix B: Existence and Uniqueness of Strong Solutions of Stochastic Delay Differential Equations References Indexshow more