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...
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Livre numérique |
| Lingua: | Anglais |
| Pubblicazione: |
New York, NY :
Springer New York : Springer e-books
[20..].
Cham : Springer Nature |
| Serie: | Stochastic Modelling and Applied Probability
58 Stochastic Modelling and Applied Probability formerly: Applications of Mathematics 58 |
| Soggetti: | |
| Accesso online: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression du document génère 446 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Stochastic ordinary and stochastic partial differential equations, transition from microscopic to macroscopic equations, Peter Kotelenez, 2008, New York, Springer Science+Business Media, 1 vol. (X-458 p.), Stochastic modelling and applied probability, 978-0-387-74316-5 |
Sommario:
- 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