Potential Theory And Right Processes
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Markov Processes And Potential Theory
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Author : Robert McCallum Blumenthal
language : en
Publisher: Courier Corporation
Release Date : 2007-01-01
Markov Processes And Potential Theory written by Robert McCallum Blumenthal and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
This graduate-level text explores the relationship between Markov processes and potential theory, in addition to aspects of the theory of additive functionals. Topics include Markov processes, excessive functions, multiplicative functionals and subprocesses, and additive functionals and their potentials. A concluding chapter examines dual processes and potential theory. 1968 edition.
Potential Theory And Right Processes
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Author : Lucian Beznea
language : en
Publisher:
Release Date : 2014-09-01
Potential Theory And Right Processes written by Lucian Beznea and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Potential Theory
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Author : Lester L. Helms
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-04-10
Potential Theory written by Lester L. Helms 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 2014-04-10 with Mathematics categories.
Potential Theory presents a clear path from calculus to classical potential theory and beyond, with the aim of moving the reader into the area of mathematical research as quickly as possible. The subject matter is developed from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem, the author develops methods for constructing solutions of Laplace's equation on a region with prescribed values on the boundary of the region. The latter half of the book addresses more advanced material aimed at those with the background of a senior undergraduate or beginning graduate course in real analysis. Starting with solutions of the Dirichlet problem subject to mixed boundary conditions on the simplest of regions, methods of morphing such solutions onto solutions of Poisson's equation on more general regions are developed using diffeomorphisms and the Perron-Wiener-Brelot method, culminating in application to Brownian motion. In this new edition, many exercises have been added to reconnect the subject matter to the physical sciences. This book will undoubtedly be useful to graduate students and researchers in mathematics, physics and engineering.
Classical Potential Theory And Its Probabilistic Counterpart
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Author : Joseph L. Doob
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-01-12
Classical Potential Theory And Its Probabilistic Counterpart written by Joseph L. Doob 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 2001-01-12 with Mathematics categories.
From the reviews: "Here is a momumental work by Doob, one of the masters, in which Part 1 develops the potential theory associated with Laplace's equation and the heat equation, and Part 2 develops those parts (martingales and Brownian motion) of stochastic process theory which are closely related to Part 1". --G.E.H. Reuter in Short Book Reviews (1985)
Potential Theory
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Author : Jürgen Bliedtner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Potential Theory written by Jürgen Bliedtner 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.
During the last thirty years potential theory has undergone a rapid development, much of which can still only be found in the original papers. This book deals with one part of this development, and has two aims. The first is to give a comprehensive account of the close connection between analytic and probabilistic potential theory with the notion of a balayage space appearing as a natural link. The second aim is to demonstrate the fundamental importance of this concept by using it to give a straight presentation of balayage theory which in turn is then applied to the Dirichlet problem. We have considered it to be beyond the scope of this book to treat further topics such as duality, ideal boundary and integral representation, energy and Dirichlet forms. The subject matter of this book originates in the relation between classical potential theory and the theory of Brownian motion. Both theories are linked with the Laplace operator. However, the deep connection between these two theories was first revealed in the papers of S. KAKUTANI [1], [2], [3], M. KAC [1] and J. L. DO DB [2] during the period 1944-54: This can be expressed by the·fact that the harmonic measures which occur in the solution of the Dirichlet problem are hitting distri butions for Brownian motion or, equivalently, that the positive hyperharmonic func tions for the Laplace equation are the excessive functions of the Brownian semi group.
Classical Potential Theory And Its Probabilistic Counterpart
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Author : Joseph L. Doob
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Classical Potential Theory And Its Probabilistic Counterpart written by Joseph L. Doob 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.
From the reviews: "This huge book written in several years by one of the few mathematicians able to do it, appears as a precise and impressive study (not very easy to read) of this bothsided question that replaces, in a coherent way, without being encyclopaedic, a large library of books and papers scattered without a uniform language. Instead of summarizing the author gives his own way of exposition with original complements. This requires no preliminary knowledge. ...The purpose which the author explains in his introduction, i.e. a deep probabilistic interpretation of potential theory and a link between two great theories, appears fulfilled in a masterly manner". M. Brelot in Metrika (1986)
Markov Processes And Potential Theory
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Author :
language : en
Publisher: Academic Press
Release Date : 2011-08-29
Markov Processes And Potential Theory written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-29 with Mathematics categories.
Markov Processes and Potential Theory
Selected Works Of Kai Lai Chung
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Author : Farid AitSahlia
language : en
Publisher: World Scientific
Release Date : 2008
Selected Works Of Kai Lai Chung written by Farid AitSahlia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This unique volume presents a collection of the extensive journal publications written by Kai Lai Chung over a span of 70-odd years. It was produced to celebrate his 90th birthday. The selection is only a subset of the many contributions that he made throughout his prolific career. Another volume, Chance and Choice, published by World Scientific in 2004, contains yet another subset, with four articles in common with this volume. Kai Lai Chung''s research contributions have had a major influence on several areas in probability. Among his most significant works are those related to sums of independent random variables, Markov chains, time reversal of Markov processes, probabilistic potential theory, Brownian excursions, and gauge theorems for the SchrAdinger equation.As Kai Lai Chung''s contributions spawned critical new developments, this volume also contains retrospective and perspective views provided by collaborators and other authors who themselves advanced the areas of probability and mathematics."
Classical Fine Potential Theory
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Author : Mohamed El Kadiri
language : en
Publisher: Springer Nature
Release Date : 2025-04-03
Classical Fine Potential Theory written by Mohamed El Kadiri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-03 with Mathematics categories.
This comprehensive book explores the intricate realm of fine potential theory. Delving into the real theory, it navigates through harmonic and subharmonic functions, addressing the famed Dirichlet problem within finely open sets of R^n. These sets are defined relative to the coarsest topology on R^n, ensuring the continuity of all subharmonic functions. This theory underwent extensive scrutiny starting from the 1970s, particularly by Fuglede, within the classical or axiomatic framework of harmonic functions. The use of methods from fine potential theory has led to solutions of important classical problems and has allowed the discovery of elegant results for extension of classical holomorphic function to wider classes of “domains”. Moreover, this book extends its reach to the notion of plurisubharmonic and holomorphic functions within plurifinely open sets of C^n and its applications to pluripotential theory. These open sets are defined by coarsest topology that renders all plurisubharmonic functions continuous on C^n. The presentation is meticulously crafted to be largely self-contained, ensuring accessibility for readers at various levels of familiarity with the subject matter. Whether delving into the fundamentals or seeking advanced insights, this book is an indispensable reference for anyone intrigued by potential theory and its myriad applications. Organized into five chapters, the first four unravel the intricacies of fine potential theory, while the fifth chapter delves into plurifine pluripotential theory.
General Theory Of Markov Processes
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Author :
language : en
Publisher: Academic Press
Release Date : 1988-11-01
General Theory Of Markov Processes written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-11-01 with Mathematics categories.
General Theory of Markov Processes