E-Book, Englisch, Band 58, 459 Seiten, eBook
Transition from Microscopic to Macroscopic Equations
E-Book, Englisch, Band 58, 459 Seiten, eBook
Reihe: Stochastic Modelling and Applied Probability
ISBN: 978-0-387-74317-2
Verlag: Springer US
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)
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Research
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Weitere Infos & Material
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.