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# ðŸ“™ Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations by Peter Kotelenez (auth.) â€” free epub

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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.

- Series:
**Stochastic Modelling and Applied Probability formerly: Applications of Mathematics 58** - Author:
**Peter Kotelenez (auth.)** - Year:
**2008** - Publisher:
**Springer-Verlag New York** - Language:
**English** - ISBN:
**3540669108**

- File size:
**2 401 242** - Format:
**pdf**

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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 oscill...

This book presents a systematic theory of Taylor expansions of evolutionary-type stochastic partial differential equations (SPDEs). The authors show how Taylor expansions can be used to derive higher order numerical methods for SPDEs, with a focus on path...

This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations I, which took place at the Centre of Mathematics of the University of Minho, Braga, Portugal, from the 5th to the 7th of December, 2012....

This book is a collection of original research papers and expository articles from the scientific program of the 2004-05 Emphasis Year on Stochastic Analysis and Partial Differential Equations at Northwestern University. Many well-known mathematicians att...

Alberto P. CalderÃ³n (1920-1998) was one of this century's leading mathematical analysts. His contributions, characterized by great originality and depth, have changed the way researchers approach and think about everything from harmonic analysis to partia...

Modeling, in particular with partial differential equations, plays an ever growing role in the applied sciences. Hence its mathematical understanding is an important issue for today's research. This book provides an introduction to three different topi...

This textbook provides a genuine treatment of ordinary and partial differential equations (ODEs and PDEs) through 50 class tested lectures.Key Features:Explains mathematical concepts with clarity and rigor, using fully worked-out examples and helpful illu...

These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technical...

Stochastic Partial Differential Equations and Applications gives an overview of current state-of-the-art stochastic PDEs in several fields, such as filtering theory, stochastic quantization, quantum probability, and mathematical finance. Featuring contrib...

The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the well-received German ...

This book reflects a significant part of authors' research activity durÂ ing the last ten years. The present monograph is constructed on the results obtained by the authors through their direct cooperation or due to the authors separately or in cooperatio...

Mathematical models are often used to describe complex phenomena such as climate change dynamics, stock market fluctuations, and the Internet. These models typically depend on estimated values of key parameters that determine system behavior. Hence it is ...

We learn by doing. We learn mathematics by doing problems. And we learn more mathematics by doing more problems. This is the sequel to Problems in Mathematical Analysis I (Volume 4 in the Student Mathematical Library series). If you want to hone your unde...

The book uses classical problems to motivate a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil and McShane, showing how new theories of integration were developed to solve problems that earlier integration theori...

The Kernel Function and Conformal Mapping by Stefan Bergman is a revised edition of The Kernel Function. The author has made extensive changes in the original volume. The present book will be of interest not only to mathematicians, but also to engineers, ...

Building on the foundation laid in the first volume of Subharmonic Functions, which has become a classic, this second volume deals extensively with applications to functions of a complex variable. The material also has applications in differential equatio...

This monograph is devoted to the study of the weighted Bergman space $A^p_\omega$ of the unit disc $\mathbb{D}$ that is induced by a radial continuous weight $\omega$ satisfying $\lim_{r\to 1^-}\frac{\int_r^1\omega(s)\,ds}{\omega(r)(1-r)}=\infty.$ Every s...

This book deals with the long-time behavior of solutions of degenerate parabolic dissipative equations arising in the study of biological, ecological, and physical problems. Examples include porous media equations, -Laplacian and doubly nonlinear equation...

This book is a reader-friendly, relatively short introduction to the modern theory of linear partial differential equations. An effort has been made to present complete proofs in an accessible and self-contained form. The first three chapters are on eleme...