Ergodicity for Infinite Dimensional Systems

This is the only book on stochastic modelling of infinite dimensional dynamical systems.

G. Da Prato (Author), J. Zabczyk (Author)

9780521579001, Cambridge University Press

Paperback, published 16 May 1996

352 pages
22.8 x 15.2 x 2 cm, 0.48 kg

"In the reviewer's opinion, the monograph provides an important contribution to the theory of stochastic infinite-dimensional systems, especially to the investigation of their asymptotic behavior....Although the authors concentrate on their own results, they also have taken an important and successful step in this direction." Bohdan Maslowski, Mathematical Reviews

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.

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.

Subject Areas: Calculus & mathematical analysis [PBK]