Stochastic Ordinary and Stochastic Partial Differential Equations
Transition from Microscopic to Macroscopic Equations
(Sprache: Englisch)
This book analyzes mathematical models of time-dependent physical phenomena on microscopic, macroscopic and mesoscopic levels. It provides a rigorous derivation of each level from the preceding one and examines the resulting mesoscopic equations in detail.
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This book analyzes mathematical models of time-dependent physical phenomena on microscopic, macroscopic and mesoscopic levels. It provides a rigorous derivation of each level from the preceding one and examines the resulting mesoscopic equations in detail.
Klappentext zu „Stochastic Ordinary and Stochastic Partial Differential Equations “
Stochastic Partial Differential Equations analyzes mathematical models of time-dependent physical phenomena on microscopic, macroscopic and mesoscopic levels. It provides a rigorous derivation of each level from the preceding one and examines the resulting mesoscopic equations in detail. Coverage first describes the transition from the microscopic equations to the mesoscopic equations. It then covers a general system for the positions of the large particles.
Inhaltsverzeichnis zu „Stochastic Ordinary and Stochastic Partial Differential Equations “
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.
Bibliographische Angaben
- Autor: Peter Kotelenez
- 2007, 2008, 459 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, New York
- ISBN-10: 0387743162
- ISBN-13: 9780387743165
- Erscheinungsdatum: 17.12.2007
Sprache:
Englisch
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