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...
Tallennettuna:
| Päätekijä: | |
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| Aineistotyyppi: | Livre numérique |
| Kieli: | Anglais |
| Julkaistu: |
New York, NY :
Springer New York : Springer e-books
[20..].
Cham : Springer Nature |
| Sarja: | Stochastic Modelling and Applied Probability
58 Stochastic Modelling and Applied Probability formerly: Applications of Mathematics 58 |
| Aiheet: | |
| Linkit: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
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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 |
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| 084 | |a 62-02. 2010 | ||
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| 100 | 1 | |a Kotelenez, Peter, |d 1943- | |
| 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, NY : |b Springer New York : |b Springer e-books. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 1 | |a Stochastic Modelling and Applied Probability |v 58 | |
| 490 | 0 | |a Stochastic Modelling and Applied Probability formerly: Applications of Mathematics |v 58 |x 0172-4568 | |
| 500 | |a L'impression du document génère 446 p. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 1 | |a 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 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 | ||
| 650 | |a Particules (physique) |x Dynamique |x Modèles mathématiques | ||
| 650 | |a Équations différentielles stochastiques | ||
| 650 | |a Équations aux dérivées partielles stochastiques | ||
| 776 | 0 | |0 12463169X |t Stochastic ordinary and stochastic partial differential equations |o transition from microscopic to macroscopic equations |f Peter Kotelenez |d 2008 |c New York |n Springer Science+Business Media |p 1 vol. (X-458 p.) |s Stochastic modelling and applied probability |z 978-0-387-74316-5 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/978-0-387-74317-2 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-6H25W12R-P |z Accès sur la plateforme Istex | |
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| 856 | 4 | |5 180339901:75088262X |u https://ezproxy.insa-cvl.fr/login?qurl=https://doi.org/10.1007/978-0-387-74317-2 |z Accès INSA CVL | |
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