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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: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York : Imprint: Springer,
2008.
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| Edición: | 1st ed. 2008. |
| Colección: | Stochastic Modelling and Applied Probability,
58 |
| Temas: | |
| Acceso en línea: | Texto Completo |
Tabla de Contenidos:
- From Microscopic Dynamics to Mesoscopic Kinematics
- Heuristics: Microscopic Model and Space-Time Scales
- Deterministic Dynamics in a Lattice Model and a Mesoscopic (Stochastic) Limit
- Proof of the Mesoscopic Limit Theorem
- Mesoscopic A: Stochastic Ordinary Differential Equations
- Stochastic Ordinary Differential Equations: Existence, Uniqueness, and Flows Properties
- Qualitative Behavior of Correlated Brownian Motions
- Proof of the Flow Property
- Comments on SODEs: A Comparison with Other Approaches
- Mesoscopic B: Stochastic Partial Differential Equations
- Stochastic Partial Differential Equations: Finite Mass and Extensions
- Stochastic Partial Differential Equations: Infinite Mass
- Stochastic Partial Differential Equations:Homogeneous and Isotropic Solutions
- Proof of Smoothness, Integrability, and Itô's Formula
- Proof of Uniqueness
- Comments on Other Approaches to SPDEs
- Macroscopic: Deterministic Partial Differential Equations
- Partial Differential Equations as a Macroscopic Limit
- General Appendix.