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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...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Kotelenez, P. (Peter), 1943- (Author)
Format: Electronic eBook
Language:Inglés
Published: New York : Springer Science+Business Media, ©2008.
Series:Stochastic modelling and applied probability ; 58.
Subjects:
Online Access:Texto completo
Table of Contents:
  • 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.