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Stochastic ordinary and stochastic partial differential equations : transition from microscopic to macroscopic equations /
This book provides the first rigorous derivation of mesoscopic and macroscopic equations from a deterministic system of microscopic equations. The microscopic equations are cast in the form of a deterministic (Newtonian) system of coupled nonlinear oscillators for N large particles and infinitely ma...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Springer Science+Business Media,
©2008.
|
| Colección: | Stochastic modelling and applied probability ;
58. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- pt. I. From Microscopic Dynamics to Mesoscopic Kinematics
- 1. Heuristics: Microscopic Model and Space-Time Scales
- 2. Deterministic Dynamics in a Lattice Model and a Mesoscopic (Stochastic) Limit
- 3. Proof of the Mesoscopic Limit Theorem
- pt. II. Mesoscopic A: Stochastic Ordinary Differential Equations
- 4. Stochastic Ordinary Differential Equations: Existence, Uniqueness, and Flows Properties
- 5. Qualitative Behavior of Correlated Brownian Motions
- 6. Proof of the Flow Property
- 7. Comments on SODEs: A Comparison with Other Approaches
- pt. III. Mesoscopic B: Stochastic Partial Differential Equations
- 8. Stochastic Partial Differential Equations: Finite Mass and Extensions
- 9. Stochastic Partial Differential Equations: Infinite Mass
- 10. Stochastic Partial Differential Equations: Homogeneous and Isotropic Solutions
- 11. Proof of Smoothness, Integrability, and Ito's Formula
- 12. Proof of Uniqueness
- 13. Comments on Other Approaches to SPDEs
- pt. IV. Macroscopic: Deterministic Partial Differential Equations
- 14. Partial Differential Equations as a Macroscopic Limit
- pt. V. General Appendix
- 15. Appendix.