Ergodicity for Infinite Dimensional Systems

This book is devoted to the asymptotic properties of solutions of stochastic evolution equations in infinite dimensional spaces. It is divided into three parts: Markovian dynamical systems; invariant measures for stochastic evolution equations; and invariant measures for specific models. The focus is on models of dynamical processes affected by white noise, which are described by partial differential equations such as the reaction-diffusion equations or Navier-Stokes equations. Besides existence and uniqueness questions, the authors pay special attention to the asymptotic behavior of the solutions, to invariant measures and ergodicity. The authors present some of the results found here for the first time. For all whose research interests involve stochastic modeling, dynamical systems, or ergodic theory, this book will be an essential purchase.

Part I. Markovian Dynamical Systems: 1. General dynamical systems; 2. Canonical Markovian systems; 3. Ergodic and mixing measures; 4. Regular Markovian systems; Part II. Invariant Measures For Stochastics For Evolution Equations: 5. Stochastic differential equations; 6. Existence of invariant measures; 7. Uniqueness of invariant measures; 8. Densities of invariant measures; Part III. Invariant Measures For Specific Models: 9. Ornstein-Uhlenbeck processes; 10. Stochastic delay systems; 11. Reaction-diffusion equations; 12. Spin systems; 13. Systems perturbed through the boundary; 14. Burgers equation; 15. Navier-Stokes equations; Appendices.