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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: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Springer Science+Business Media,
©2008.
|
| Colección: | Stochastic modelling and applied probability ;
58. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Kotelenez, P. |q (Peter), |d 1943- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjrT9MkcYkfh7BC6j38Qv3 | |
| 245 | 1 | 0 | |a Stochastic ordinary and stochastic partial differential equations : |b transition from microscopic to macroscopic equations / |c Peter Kotelenez. |
| 260 | |a New York : |b Springer Science+Business Media, |c ©2008. | ||
| 300 | |a 1 online resource (x, 458 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Stochastic modelling and applied probability ; |v 58 | |
| 504 | |a Includes bibliographical references (pages 445-458) and index. | ||
| 505 | 0 | |a 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. | |
| 520 | |a 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 many small particles. The mesoscopic equations are stochastic ordinary differential equations (SODEs) and stochastic partial differential equatuions (SPDEs), and the macroscopic limit is described by a parabolic partial differential equation. A detailed analysis of the SODEs and (quasi-linear) SPDEs is presented. Semi-linear (parabolic) SPDEs are represented as first order stochastic transport equations driven by Stratonovich differentials. The time evolution of correlated Brownian motions is shown to be consistent with the depletion phenomena experimentally observed in colloids. A covariance analysis of the random processes and random fields as well as a review section of various approaches to SPDEs are also provided. An extensive appendix makes the book accessible to both scientists and graduate students who may not be specialized in stochastic analysis. Probabilists, mathematical and theoretical physicists as well as mathematical biologists and their graduate students will find this book useful. Peter Kotelenez is a professor of mathematics at Case Western Reserve University in Cleveland, Ohio. | ||
| 546 | |a English. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Stochastic differential equations. | |
| 650 | 0 | |a Stochastic partial differential equations. | |
| 650 | 6 | |a Équations différentielles stochastiques. | |
| 650 | 6 | |a Équations aux dérivées partielles stochastiques. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 0 | 7 | |a Stochastic partial differential equations. |2 cct |
| 650 | 0 | 7 | |a Équations différentielles stochastiques. |2 cct |
| 650 | 0 | 7 | |a Équations aux dérivées partielles stochastiques. |2 cct |
| 650 | 0 | 7 | |a Stochastic differential equations. |2 cct |
| 650 | 0 | 7 | |a Ecuaciones diferenciales estocásticas |2 embucm |
| 650 | 7 | |a Stochastic differential equations |2 fast | |
| 650 | 7 | |a Stochastic partial differential equations |2 fast | |
| 758 | |i has work: |a Stochastic ordinary and stochastic partial differential equations (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFPv7Q8dkrKYgwHjJxXPQq |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Kotelenez, P. (Peter), 1943- |t Stochastic ordinary and stochastic partial differential equations. |d New York : Springer Science+Business Media, ©2008 |z 9780387743165 |z 0387743162 |w (DLC) 2007940371 |w (OCoLC)172984133 |
| 830 | 0 | |a Stochastic modelling and applied probability ; |v 58. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=337049 |z Texto completo |
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