Green Brown And Probability Brownian Motion On The Line
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Green Brown And Probability Brownian Motion On The Line
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Author : Kai Lai Chung
language : en
Publisher: World Scientific
Release Date : 2002
Green Brown And Probability Brownian Motion On The Line written by Kai Lai Chung and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This invaluable book consists of two parts. Part I is the second edition of the author's widely acclaimed publication Green, Brown, and Probability, which first appeared in 1995. In this exposition the author reveals, from a historical perspective, the beautiful relations between the Brownian motion process in probability theory and two important aspects of the theory of partial differential equations initiated from the problems in electricity ? Green's formula for solving the boundary value problem of Laplace equations and the Newton-Coulomb potential.Part II of the book comprises lecture notes based on a short course on ?Brownian Motion on the Line? which the author has given to graduate students at Stanford University. It emphasizes the methodology of Brownian motion in the relatively simple case of one-dimensional space. Numerous exercises are included.
Green Brown And Probability And Brownian Motion On The Line
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Author : Kai Lai Chung
language : en
Publisher: World Scientific Publishing Company
Release Date : 2002-05-06
Green Brown And Probability And Brownian Motion On The Line written by Kai Lai Chung and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-06 with Mathematics categories.
This invaluable book consists of two parts. Part I is the second edition of the author's widely acclaimed publication Green, Brown, and Probability, which first appeared in 1995. In this exposition the author reveals, from a historical perspective, the beautiful relations between the Brownian motion process in probability theory and two important aspects of the theory of partial differential equations initiated from the problems in electricity — Green's formula for solving the boundary value problem of Laplace equations and the Newton–Coulomb potential. Part II of the book comprises lecture notes based on a short course on “Brownian Motion on the Line” which the author has given to graduate students at Stanford University. It emphasizes the methodology of Brownian motion in the relatively simple case of one-dimensional space. Numerous exercises are included.
Green Brown And Probability
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Author : Kai Lai Chung
language : en
Publisher: World Scientific
Release Date : 1995
Green Brown And Probability written by Kai Lai Chung and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
This volume shows modern probabilistic methods in action: Brownian Motion Process as applied to the electrical phenomena investigated by Green et al., beginning with the Newton-Coulomb potential and ending with solutions by first and last exits of Brownian paths from conductors.
Lectures From Markov Processes To Brownian Motion
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Author : Kai Lai Chung
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Lectures From Markov Processes To Brownian Motion written by Kai Lai Chung 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 2013-11-11 with Mathematics categories.
This book evolved from several stacks of lecture notes written over a decade and given in classes at slightly varying levels. In transforming the over lapping material into a book, I aimed at presenting some of the best features of the subject with a minimum of prerequisities and technicalities. (Needless to say, one man's technicality is another's professionalism. ) But a text frozen in print does not allow for the latitude of the classroom; and the tendency to expand becomes harder to curb without the constraints of time and audience. The result is that this volume contains more topics and details than I had intended, but I hope the forest is still visible with the trees. The book begins at the beginning with the Markov property, followed quickly by the introduction of option al times and martingales. These three topics in the discrete parameter setting are fully discussed in my book A Course In Probability Theory (second edition, Academic Press, 1974). The latter will be referred to throughout this book as the Course, and may be considered as a general background; its specific use is limited to the mate rial on discrete parameter martingale theory cited in § 1. 4. Apart from this and some dispensable references to Markov chains as examples, the book is self-contained.
Brownian Motion
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Author : Peter Mörters
language : en
Publisher: Cambridge University Press
Release Date : 2010-03-25
Brownian Motion written by Peter Mörters 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 2010-03-25 with Mathematics categories.
This 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.
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. The experiments were successful in determining the mean kinetic energy of the granules of Brownian motion; however, the values for molecular magnitudes Perrin inferred from them simply presupposed that the granule mean kinetic energy was the same as the mean molecular kinetic energy in the fluid in which the granules move. This stipulation became increasingly questionable in the years between 1908 and 1913, as significantly lower values for these magnitudes were obtained from other experimental results like alpha-particle emissions, ionization, and Planck's blackbody radiation equation. 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. The practice of theory-mediated measurement in physics had a long history before 1900, but the concerted efforts of Perrin, Rutherford, Millikan, Planck, and their colleagues led to the central role this form of evidence has had in microphysical research ever since. Seth and Smith's study thus replaces an untenable legend with an account that is not only tenable, but more instructive about what the evidence did and did not show.
Einstein 1905 2005
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Author : Thibault Damour
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
Einstein 1905 2005 written by Thibault Damour 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 2006-04-18 with Science categories.
This book is the fourth in a series of lectures of the S ́ eminaire Poincar ́ e,whichis directed towards a large audience of physicists and of mathematicians. The goal of this seminar is to provide up-to-date information about general topics of great interest in physics. Both the theoretical and experimental aspects are covered, with some historical background. Inspired by the Bourbaki seminar in mathematics in its organization, hence nicknamed “Bourbaphi”, the Poincar ́ e Seminar is held twice a year at the Institut Henri Poincar ́ e in Paris, with cont- butions prepared in advance. Particular care is devoted to the pedagogical nature of the presentations so as to ful?ll the goal of being readable by a large audience of scientists. This volume contains the seventh such Seminar, held in 2005. It is devoted to Einstein’s 1905 papers and their legacy. After a presentation of Einstein’s ep- temological approach to physics, and the genesis of special relativity, a cen- nary perspective is o?ered. The geometry of relativistic spacetime is explained in detail. Single photon experiments are presented, as a spectacular realization of Einstein’s light quanta hypothesis. A previously unpublished lecture by Einstein, which presents an illuminating point of view on statistical physics in 1910, at the dawn of quantum mechanics, is reproduced. The volume ends with an essay on the historical, physical and mathematical aspects of Brownian motion. We hopethatthe publicationofthis serieswill servethe community ofphy- cists and mathematicians at the graduate student or professional level.
Mathematical Methods For Financial Markets
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Author : Monique Jeanblanc
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-03
Mathematical Methods For Financial Markets written by Monique Jeanblanc 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 2009-10-03 with Business & Economics categories.
Mathematical finance has grown into a huge area of research which requires a large number of sophisticated mathematical tools. This book simultaneously introduces the financial methodology and the relevant mathematical tools in a style that is mathematically rigorous and yet accessible to practitioners and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissible strategies, contingent claims, option pricing and default risk with the mathematical theory of Brownian motion, diffusion processes, and Lévy processes. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes. The extensive bibliography comprises a wealth of important references and the author index enables readers quickly to locate where the reference is cited within the book, making this volume an invaluable tool both for students and for those at the forefront of research and practice.
Introduction To Random Time And Quantum Randomness New Edition
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Author : Kai Lai Chung
language : en
Publisher: World Scientific
Release Date : 2003-05-28
Introduction To Random Time And Quantum Randomness New Edition written by Kai Lai Chung and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-28 with Mathematics categories.
This book is made up of two essays on the role of time in probability and quantum physics. In the first one, K L Chung explains why, in his view, probability theory starts where random time appears. This idea is illustrated in various probability schemes and the deep impact of those random times on the theory of the stochastic process is shown.In the second essay J-C Zambrini shows why quantum physics is not a regular probabilistic theory, but also why stochastic analysis provides new tools for analyzing further the meaning of Feynman's path integral approach and a number of foundational issues of quantum physics far beyond what is generally considered. The role of the time parameter, in this theory, is critically re-examined and a fresh way to approach the long-standing problem of the quantum time observable is suggested.
Chance And Choice Memorabilia
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Author : Kai Lai Chung
language : en
Publisher: World Scientific
Release Date : 2004-10-29
Chance And Choice Memorabilia written by Kai Lai Chung and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-29 with Mathematics categories.
This book begins with a historical essay entitled “Will the Sun Rise Again?” and ends with a general address entitled “Mathematics and Applications”. The articles cover an interesting range of topics: combinatoric probabilities, classical limit theorems, Markov chains and processes, potential theory, Brownian motion, Schrödinger-Feynman problems, etc. They include many addresses presented at international conferences and special seminars, as well as memorials to and reminiscences of prominent contemporary mathematicians and reviews of their works. Rare old photos of many of them enliven the book.