DMCA. Copyrighted Work that you can Claim.
Base have 820 524 books.
Search: 


📙 Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations by Peter Kotelenez (auth.) — free epub


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.



About file:

  • File size: 2 401 242
  • Format: pdf


Security code:
Download button

Similar books results


Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations
Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations free epub by Peter Kotelenez (auth.)

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...

Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations
Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations download pdf by Peter Kotelenez (auth.)

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...

Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations
Stochastic Ordinary and Stochastic Partial Differential Equations: Transition from Microscopic to Macroscopic Equations pdf free by Peter Kotelenez (auth.)

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...

Taylor Approximations for Stochastic Partial Differential Equations (CBMS-NSF Regional Conference Series in Applied Mathematics)
Taylor Approximations for Stochastic Partial Differential Equations (CBMS-NSF Regional Conference Series in Applied Mathematics) free epub by Arnulf Jentzen and Peter Kloeden

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...

Taylor Approximations for Stochastic Partial Differential Equations
Taylor Approximations for Stochastic Partial Differential Equations pdf free by Arnulf Jentzen and Peter Kloeden

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...

Harmonic Analysis and Partial Differential Equations: Proceedings of a Conference Held April 4-5, 1988
Harmonic Analysis and Partial Differential Equations: Proceedings of a Conference Held April 4-5, 1988 pdf free by Conference on Harmonic Analysis and Partial Differential Equations (1988 : Florida Atlantic University), Tomas Schonbek (ed.)

This book brings together ten papers presented at the Conference on Harmonic Analysis and Partial Differential Equations, held in April 1988 at Florida Atlantic University. The papers illuminate the relationship between harmonic analysis and partial diffe...

From Particle Systems to Partial Differential Equations: Particle Systems and PDEs, Braga, Portugal, December 2012
From Particle Systems to Partial Differential Equations: Particle Systems and PDEs, Braga, Portugal, December 2012 pdf free by Cédric Bernardin, Patricia Gonçalves (eds.)

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....

Stochastic Analysis and Partial Differential Equations: Emphasis Year 2004 - 2005 on Stochastic Analysis and Partial Differential Equations ... Evanston, Illinois
Stochastic Analysis and Partial Differential Equations: Emphasis Year 2004 - 2005 on Stochastic Analysis and Partial Differential Equations ... Evanston, Illinois pdf free by Gui-Qiang Chen, Elton Hsu, Mark Pinsky (ed.)

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...

Optimization Methods in Partial Differential Equations: Proceedings from the 1996 Joint Summer Research Conference, June 16-20, 1996, Mt. Holyoke College
Optimization Methods in Partial Differential Equations: Proceedings from the 1996 Joint Summer Research Conference, June 16-20, 1996, Mt. Holyoke College epub download by Steven Cox, Irena Lasiecka (ed.)

This book presents a collection of papers written by specialists in the field and devoted to the analysis of various aspects of optimization problems with a common focus on partial differential equation (PDE) models. These papers were presented at the AMS...