Liu Stability of Infinite Dimensional Stochastic Differential Equations with Applications

Erscheinungsjahr 2005
ISBN: 978-1-4200-3482-0
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 312 Seiten

Reihe: Monographs and Surveys in Pure and Applied Mathematics

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.

Zielgruppe

Graduate students, researchers, engineers, and scientists in stochastic differential equations and probability theory.

Autoren/Hrsg.

Liu, Kai

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

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
Index