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Author: Frank B. Knight
Publisher: American Mathematical Soc.
Published: 1981
Total Pages: 220
ISBN-13: 0821815180
DOWNLOAD EBOOKPresents some gratuitous generalities on scientific method as it relates to diffusion theory. This book defines Brownian motion by the characterization of P Levy, and then constructed in three basic ways and these are proved to be equivalent in the appropriate sense.
Author: Daniel Thomas Gillespie
Publisher: OUP Oxford
Published: 2012-10-18
Total Pages: 336
ISBN-13: 0191641537
DOWNLOAD EBOOKBrownian diffusion is the motion of one or more solute molecules in a sea of very many, much smaller solvent molecules. Its importance today owes mainly to cellular chemistry, since Brownian diffusion is one of the ways in which key reactant molecules move about inside a living cell. This book focuses on the four simplest models of Brownian diffusion: the classical Fickian model, the Einstein model, the discrete-stochastic (cell-jumping) model, and the Langevin model. The authors carefully develop the theories underlying these models, assess their relative advantages, and clarify their conditions of applicability. Special attention is given to the stochastic simulation of diffusion, and to showing how simulation can complement theory and experiment. Two self-contained tutorial chapters, one on the mathematics of random variables and the other on the mathematics of continuous Markov processes (stochastic differential equations), make the book accessible to researchers from a broad spectrum of technical backgrounds.
Author: David Freedman
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 242
ISBN-13: 146156574X
DOWNLOAD EBOOKA long time ago I started writing a book about Markov chains, Brownian motion, and diffusion. I soon had two hundred pages of manuscript and my publisher was enthusiastic. Some years and several drafts later, I had a thot:sand pages of manuscript, and my publisher was less enthusiastic. So we made it a trilogy: Markov Chains Brownian Motion and Diffusion Approximating Countable Markov Chains familiarly - Me, B & D, and ACM. I wrote the first two books for beginning graduate students with some knowledge of probability; if you can follow Sections 3.4 to 3.9 of Brownian Motion and Diffusion you're in. The first two books are quite independent of one another, and completely independent of the third. This last book is a monograph, which explains one way to think about chains with instantaneous states. The results in it are supposed to be new, except where there are spe cific disclaimers; it's written in the framework of Markov Chains. Most of the proofs in the trilogy are new, and I tried hard to make them explicit. The old ones were often elegant, but I seldom saw what made them go. With my own, I can sometimes show you why things work. And, as I will argue in a minute, my demonstrations are easier technically. If I wrote them down well enough, you may come to agree.
Author: Peter Mörters
Publisher: Cambridge University Press
Published: 2010-03-25
Total Pages:
ISBN-13: 1139486578
DOWNLOAD EBOOKThis eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.
Author: Kiyosi Itô
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 341
ISBN-13: 3642620256
DOWNLOAD EBOOKSince its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.
Author: Leonardo Dagdug
Publisher: Springer
Published: 2024-02-22
Total Pages: 0
ISBN-13: 9783031464744
DOWNLOAD EBOOKThis book offers the reader a journey through the counterintuitive nature of Brownian motion under confinement. Diffusion is a universal phenomenon that controls a wide range of physical, chemical, and biological processes. The transport of spatially-constrained molecules and small particles is ubiquitous in nature and technology and plays an essential role in different processes. Understanding the physics of diffusion under conditions of confinement is essential for a number of biological phenomena and potential technological applications in micro- and nanofluidics, among others. Studies on diffusion under confinement are typically difficult to understand for young scientists and students because of the extensive background on diffusion processes, physics, and mathematics that is required. All of this information is provided in this book, which is essentially self-contained as a result of the authors’ efforts to make it accessible to an audience of students from a variety of different backgrounds. The book also provides the necessary mathematical details so students can follow the technical process required to solve each problem. Readers will also find detailed explanations of the main results based on the last 30 years of research devoted to studying diffusion under confinement. The authors approach the physical problem from various angles and discuss the role of geometries and boundary conditions in diffusion. This textbook serves as a comprehensive and modern overview of Brownian motion under confinement and is intended for young scientists, graduate students, and advanced undergraduates in physics, physical chemistry, biology, chemistry, chemical engineering, biochemistry, bioengineering, and polymer and material sciences.
Author: Edward Nelson
Publisher: Princeton University Press
Published: 1967-02-21
Total Pages: 147
ISBN-13: 0691079501
DOWNLOAD EBOOKThese notes are based on a course of lectures given by Professor Nelson at Princeton during the spring term of 1966. The subject of Brownian motion has long been of interest in mathematical probability. In these lectures, Professor Nelson traces the history of earlier work in Brownian motion, both the mathematical theory, and the natural phenomenon with its physical interpretations. He continues through recent dynamical theories of Brownian motion, and concludes with a discussion of the relevance of these theories to quantum field theory and quantum statistical mechanics.
Author: David Freedman
Publisher:
Published: 1970
Total Pages: 243
ISBN-13:
DOWNLOAD EBOOKThe book is part of a trilogy covering the field of Markov processes and provides a readable and constructive treatment of Brownian motion and diffusion. It contains some of the author's own research and many of the proofs are new. It dispenses with most of the customary transform apparatus, and the chapter on Brownian motion emphasizes topics which haven't had much textbook coverage, such as square variation, the reflection principle, and the invariance principle. The chapter on diffusion shows how to obtain the process from Brownian by changing time. (Author).
Author: Grigorios A. Pavliotis
Publisher: Springer
Published: 2014-11-19
Total Pages: 345
ISBN-13: 1493913239
DOWNLOAD EBOOKThis book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.
Author:
Publisher:
Published: 1997
Total Pages: 201
ISBN-13:
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