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Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations: 58 - Rilegato
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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.
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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.
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Stochastic Ordinary and Stochastic Partial Differential Equations : Transition from Microscopic to Macroscopic Equations. Stochastic Modelling and Applied Probability ; 58
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Berlin : Springer New York - Berlin : Springer Berlin, 2007
ISBN 10: 0387743162
ISBN 13: 9780387743165
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Analyzes mathematical models of time-dependent physical phenomena on three levels including microscopic, mesoscopic and macroscopic.Stochastic Partial Differential Equations analyzes mathematical models of time-dependent physical phenomena on . Codice articolo 5910872
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 472 pp. Englisch. Codice articolo 9780387743165
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