Brownian Motion
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Aspects Of Brownian Motion
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Author : Roger Mansuy
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-16
Aspects Of Brownian Motion written by Roger Mansuy 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 2008-09-16 with Mathematics categories.
Stochastic calculus and excursion theory are very efficient tools for obtaining either exact or asymptotic results about Brownian motion and related processes. This book focuses on special classes of Brownian functionals, including Gaussian subspaces of the Gaussian space of Brownian motion; Brownian quadratic funtionals; Brownian local times; Exponential functionals of Brownian motion with drift; Time spent by Brownian motion below a multiple of its one-sided supremum.
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.
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.
Brownian Motion
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Author : René L. Schilling
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-08-22
Brownian Motion written by René L. Schilling and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-22 with Mathematics categories.
Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance. Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authors’ aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs. This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion.
Handbook Of Brownian Motion Facts And Formulae
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Author : Andrei N. Borodin
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Handbook Of Brownian Motion Facts And Formulae written by Andrei N. Borodin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
There are two parts in this book. The first part is devoted mainly to the proper ties of linear diffusions in general and Brownian motion in particular. The second part consists of tables of distributions of functionals of Brownian motion and re lated processes. The primary aim of this book is to give an easy reference to a large number of facts and formulae associated to Brownian motion. We have tried to do this in a "handbook-style". By this we mean that results are given without proofs but are equipped with a reference where a proof or a derivation can be found. It is our belief and experience that such a material would be very much welcome by students and people working with applications of diffusions and Brownian motion. In discussions with many of our colleagues we have found that they share this point of view. Our original plan included more things than we were able to realize. It turned out very soon when trying to put the plan into practice that the material would be too wide to be published under one cover. Excursion theory, which most of the recent results concerning linear Brownian motion and diffusions can be classified as, is only touched upon slightly here, not to mention Brownian motion in several dimensions which enters only through the discussion of Bessel processes. On the other hand, much attention is given to the theory of local time.
Brownian Motion And Molecular Reality
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Author : George E. Smith
language : en
Publisher: Oxford University Press
Release Date : 2020-08-14
Brownian Motion And Molecular Reality written by George E. Smith and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-14 with Science categories.
Between 1905 and 1913, French physicist Jean Perrin's experiments on Brownian motion ostensibly put a definitive end to the long debate regarding the real existence of molecules, proving the atomic theory of matter. While Perrin's results had a significant impact at the time, later examination of his experiments questioned whether he really gained experimental access to the molecular realm. In this case study in the history and philosophy of science, George E. Smith and Raghav Seth here argue that despite doubts, Perrin's measurements were nevertheless exemplars of theory-mediated measurement-the practice of obtaining values for an inaccessible quantity by inferring them from an accessible proxy via theoretical relationships between them. They argue that it was actually Perrin more than any of his contemporaries who championed this approach during the years in question.
Brownian Motion
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Author : Robert M. Mazo
language : en
Publisher: OUP Oxford
Release Date : 2008-10-23
Brownian Motion written by Robert M. Mazo and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-23 with Science categories.
Brownian motion - the incessant motion of small particles suspended in a fluid - is an important topic in statistical physics and physical chemistry. This book studies its origin in molecular scale fluctuations, its description in terms of random process theory and also in terms of statistical mechanics. A number of new applications of these descriptions to physical and chemical processes, as well as statistical mechanical derivations and the mathematical background are discussed in detail. Graduate students, lecturers, and researchers in statistical physics and physical chemistry will find this an interesting and useful reference work.
Handbook Of Brownian Motion
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Author : Andrei Borodin
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Handbook Of Brownian Motion written by Andrei Borodin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
There are two parts in this book. The first part is devoted mainly to the proper ties of linear diffusions in general and Brownian motion in particular. The second part consists of tables of distributions of functionals of Brownian motion and re lated processes. The primary aim of this book is to give an easy reference to a large number of facts and formulae associated to Brownian motion. We have tried to do this in a "handbook-style". By this we mean that results are given without proofs but are equipped with a reference where a proof or a derivation can be found. It is our belief and experience that such a material would be very much welcome by students and people working with applications of diffusions and Brownian motion. In discussions with many of our colleagues we have found that they share this point of view. Our original plan included more things than we were able to realize. It turned out very soon when trying to put the plan into practice that the material would be too wide to be published under one cover. Excursion theory, which most of the recent results concerning linear Brownian motion and diffusions can be classified as, is only touched upon slightly here, not to mention Brownian motion in several dimensions which enters only through the discussion of Bessel processes. On the other hand, much attention is given to the theory of local time.
Continuous Martingales And Brownian Motion
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Author : Daniel Revuz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Continuous Martingales And Brownian Motion written by Daniel Revuz 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 2013-06-29 with Mathematics categories.
This book focuses on the probabilistic theory ofBrownian motion. This is a good topic to center a discussion around because Brownian motion is in the intersec tioll of many fundamental classes of processes. It is a continuous martingale, a Gaussian process, a Markov process or more specifically a process with in dependent increments; it can actually be defined, up to simple transformations, as the real-valued, centered process with independent increments and continuous paths. It is therefore no surprise that a vast array of techniques may be success fully applied to its study and we, consequently, chose to organize the book in the following way. After a first chapter where Brownian motion is introduced, each of the following ones is devoted to a new technique or notion and to some of its applications to Brownian motion. Among these techniques, two are of para mount importance: stochastic calculus, the use ofwhich pervades the whole book and the powerful excursion theory, both of which are introduced in a self contained fashion and with a minimum of apparatus. They have made much easier the proofs of many results found in the epoch-making book of Itö and McKean: Diffusion Processes and their Sampie Paths, Springer (1965).