Green Brown And Probability And Brownian Motion On The Line

Author : Kai Lai Chung
Publisher : World Scientific
ISBN 13 : 9789810246907
Total Pages : 184 pages
Book Rating : 4.00/5 ( download)

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Download or read book Green, Brown, and Probability & Brownian Motion on the Line written by Kai Lai Chung and published by World Scientific. This book was released on 2002 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Kai Lai Chung
Publisher : World Scientific Publishing Company
ISBN 13 : 9813102527
Total Pages : 180 pages
Book Rating : 4.21/5 ( download)

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Download or read book Green, Brown, and Probability and Brownian Motion on the Line written by Kai Lai Chung and published by World Scientific Publishing Company. This book was released on 2002-05-06 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Kai Lai Chung
Publisher : World Scientific
ISBN 13 : 9789810225339
Total Pages : 124 pages
Book Rating : 4.34/5 ( download)

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Download or read book Green, Brown, and Probability written by Kai Lai Chung and published by World Scientific. This book was released on 1995 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Peter Mörters
Publisher : Cambridge University Press
ISBN 13 : 1139486578
Total Pages : pages
Book Rating : 4.76/5 ( download)

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Download or read book Brownian Motion written by Peter Mörters and published by Cambridge University Press. This book was released on 2010-03-25 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Kai Lai Chung
Publisher :
ISBN 13 : 9781475717778
Total Pages : 252 pages
Book Rating : 4.76/5 ( download)

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Download or read book Lectures from Markov Processes to Brownian Motion written by Kai Lai Chung and published by . This book was released on 2014-01-15 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : George E. Smith
Publisher : Oxford University Press
ISBN 13 : 0190098031
Total Pages : 288 pages
Book Rating : 4.32/5 ( download)

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Download or read book Brownian Motion and Molecular Reality written by George E. Smith and published by Oxford University Press. This book was released on 2020-08-14 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Thibault Damour
Publisher : Springer Science & Business Media
ISBN 13 : 3764374365
Total Pages : 301 pages
Book Rating : 4.65/5 ( download)

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Download or read book Einstein, 1905-2005 written by Thibault Damour and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Monique Jeanblanc
Publisher : Springer Science & Business Media
ISBN 13 : 1846287375
Total Pages : 754 pages
Book Rating : 4.74/5 ( download)

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Download or read book Mathematical Methods for Financial Markets written by Monique Jeanblanc and published by Springer Science & Business Media. This book was released on 2009-10-03 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Kai Lai Chung
Publisher : World Scientific
ISBN 13 : 9814485861
Total Pages : 225 pages
Book Rating : 4.69/5 ( download)

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Download or read book Introduction To Random Time And Quantum Randomness (New Edition) written by Kai Lai Chung and published by World Scientific. This book was released on 2003-05-28 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Kai Lai Chung
Publisher : World Scientific
ISBN 13 : 9814482013
Total Pages : 327 pages
Book Rating : 4.11/5 ( download)

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Download or read book Chance And Choice: Memorabilia written by Kai Lai Chung and published by World Scientific. This book was released on 2004-10-29 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.