I. Markovian Dynamical Systems. 1. General Dynamical Systems. 2. Canonical Markovian Systems. 3. Ergodic and mixing measures. 4. Regular Markovian systems -- II. Invariant measures for stochastic evolution equations. 5. Stochastic Differential Equations. 6. Existence of invariant measures. 7. Uniqueness of invariant measures. 8. Densities of invariant measures -- 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 -- IV. Appendices -- A Smoothing properties of convolutions -- B An estimate on modulus of continuity -- C A result on implicit functions
Summary
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; 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, special attention is paid to the asymptotic behaviour of the solutions, to invariant measures and ergodicity. Some of the results found here are presented for the first time. For all whose research interests involve stochastic modelling, dynamical systems, or ergodic theory, this book will be an essential purchase
Bibliography
Includes bibliographical references (pages 321-337) and index
