Brownian Motion And Diffusion
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Brownian Motion And Diffusion
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Author : David Freedman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Brownian Motion And Diffusion written by David Freedman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A 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.
Essentials Of Brownian Motion And Diffusion
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Author : Frank B. Knight
language : en
Publisher: American Mathematical Soc.
Release Date : 1981
Essentials Of Brownian Motion And Diffusion written by Frank B. Knight and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
This work was first drafted five years ago at the invitation of the editors of the ""Encyclopedia of Mathematics and its Applications"". However, it was found to contain insufficient physical applications for that series; hence, it has finally come to rest at the doorstep of the American Mathematical Society. The first half of the work is little changed from the original, a fact which may partly explain both the allusions to applications and the elementary approach. It was written to be understood by a reader having minimal familiarity with continuous time stochastic processes. The most advanced prerequisite is an understanding of discrete parameter martingale convergence theorem.This book contains a general summary and outline, and an introduction. It presents some gratuitous generalities on scientific method as it relates to diffusion theory. Brownian motion is defined by the characterization of P. Levy. Then it is constructed in three basic ways and these are proved to be equivalent in the appropriate sense. Uniqueness theorem. Projective invariance and the Brownian bridge is presented. Probabilistic and absolute properties are distinguished. Among the former includes the distribution of the maximum, first passage time distributions, and fitting probabilities, and among the latter includes law of created logarithm, quadratic variation, Holder continuity, non-recurrence for $r\geq 2$. 3.General methods of Markov processes are adapted to diffusion. Analytic and probabilistic methods are distinguished. Among the former include transition functions, semigroups, generators, resolvents. Among the latter include Markov properties, stopping times, zero-or-one laws, Dynkin's formula, additive functionals. The book features classical modifications of Brownian motion; absorption and the dirichlet problem; space-time process and the heat equation; killed processes, Green functions, and the distributions of additive sectionals; and, time-change theorem (classical case), parabolic equations and their solution semigroups, some basic examples, distribution of passage times.The book covers Local time: construction by random walk embedding; Local time processes; Trotter's theorem; The Brownian flow; Brownian excursions; The zero set and Levy's equivalence theorem; Local times of classical diffusions; and, Sample path properties. It also includes boundary conditions for Brownian motion; the general boundary conditions; construction of the processes using local time; and, green functions and eigenfunction expansions (compact case).Another chapter is a 'finale' on nonsingular diffusion. The generators $(d/dm)(d^+/dx^+)$ are characterized. The diffusions on open intervals are constructed. The conservative boundary conditions are obtained and their diffusions are constructed. The general additive functionals and nonconservative diffusions are developed and expressed in terms of Brownian motions. The audience for this survey includes anyone who desires an introduction to Markov processes with continuous paths that is both coherent and elementary. The approach is from the particular to the general. Each method is first explained in the simplest case and supported by examples. Therefore, the book should be readily understandable to anyone with a first course in measure-theoretic probability.
Simple Brownian Diffusion
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Author : Daniel Thomas Gillespie
language : en
Publisher: OUP Oxford
Release Date : 2012-10-18
Simple Brownian Diffusion written by Daniel Thomas Gillespie and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-18 with Science categories.
Brownian 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.
Brownian Motion And Diffusion
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Author : David Freedman
language : en
Publisher:
Release Date : 1970
Brownian Motion And Diffusion written by David Freedman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.
The 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).
Relativistic Brownian Motion And Diffusion Processes
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Author : Jörn Dunkel
language : en
Publisher:
Release Date : 2008
Relativistic Brownian Motion And Diffusion Processes written by Jörn Dunkel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Dynamical Theories Of Brownian Motion
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Author : Edward Nelson
language : en
Publisher: Princeton University Press
Release Date : 1967-02-21
Dynamical Theories Of Brownian Motion written by Edward Nelson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967-02-21 with Mathematics categories.
These 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.
Diffusion Sub Diffusion And Escape
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Author : Thomas Gray
language : en
Publisher:
Release Date : 2021
Diffusion Sub Diffusion And Escape written by Thomas Gray and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
Investigations On The Theory Of The Brownian Movement
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Author : Albert Einstein
language : en
Publisher: Courier Corporation
Release Date : 1956-01-01
Investigations On The Theory Of The Brownian Movement written by Albert Einstein and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956-01-01 with Science categories.
Five early papers evolve theory that won Einstein a Nobel Prize: "Movement of Small Particles Suspended in a Stationary Liquid Demanded by the Molecular-Kinetic Theory of Heat"; "On the Theory of the Brownian Movement"; "A New Determination of Molecular Dimensions"; "Theoretical Observations on the Brownian Motion"; and "Elementary Theory of the Brownian Motion."
Scheduling And Control Of Queueing Networks
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Author : Gideon Weiss
language : en
Publisher: Cambridge University Press
Release Date : 2021-10-14
Scheduling And Control Of Queueing Networks written by Gideon Weiss and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-14 with Business & Economics categories.
A graduate text on theory and methods using applied probability techniques for scheduling service, manufacturing, and information networks.
Diffusion Under Confinement
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Author : Leonardo Dagdug
language : en
Publisher: Springer Nature
Release Date : 2024-02-01
Diffusion Under Confinement written by Leonardo Dagdug and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-01 with Science categories.
This 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 avariety 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.