Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations: 58 (Stochastic Modelling and Applied Probability) - Tapa dura

Kotelenez, Peter

 
9780387743165: Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations: 58 (Stochastic Modelling and Applied Probability)
Tapa dura
ISBN 10: 0387743162 ISBN 13: 9780387743165
Editorial: Springer, 2007

Sinopsis

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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De la contraportada

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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Editorial
Springer
Año de publicación
2007
Idioma
Inglés
ISBN 10 
0387743162
ISBN 13 
9780387743165
Encuadernación
Tapa dura
Número de páginas
472
Contacto del fabricante
no disponible
Persona responsable
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Friedrich-Karl-Str. 9
Hamburg
Alemania

Otras ediciones populares con el mismo título

9781489986580: Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations: 58 (Stochastic Modelling and Applied Probability)

Edición Destacada

ISBN 10:  1489986588 ISBN 13:  9781489986580
Editorial: Springer, 2014
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