Download or read book A Probabilities and Potential written by C. Dellacherie and published by Elsevier. This book was released on 1979-01-01 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilities and Potential, A

Download or read book Probabilities and Potential B written by C. Dellacherie and published by Elsevier. This book was released on 2011-08-18 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilities and Potential, B

Download or read book Probabilities and Potential written by Claude Dellacherie and published by . This book was released on 1982 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probabilities and Potential C written by C. Dellacherie and published by Elsevier. This book was released on 2011-08-18 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume of the monograph examines potential theory. The first chapter develops potential theory with respect to a single kernel (or discrete time semigroup). All the essential ideas of the theory are presented: excessive functions, reductions, sweeping, maximum principle. The second chapter begins with a study of the notion of reduction in the most general situation possible - the ``gambling house'' of Dubins and Savage. The beautiful results presented have never been made accessible to a wide public. These are then connected with the theory of sweeping with respect to a cone of continuous functions, and the integral representation in compact convex sets. The third chapter presents new or little-known results, with the aim of illustrating the effectiveness of capacitary methods in the most varied fields. The last two chapters are concerned with the theory of resolvents.The fourth and last part of the English edition will be devoted to the theory of Markov processes.

Download or read book Probabilities and Potential written by Claude Dellacherie and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Potential Theory written by Lester L. Helms and published by Springer Science & Business Media. This book was released on 2014-04-10 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Probabilities and Potential written by Claude Dellacherie and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probabilities and Potential written by Claude Dellacherie and published by . This book was released on 1978 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Classical Potential Theory and Its Probabilistic Counterpart written by J. L. Doob and published by Springer Science & Business Media. This book was released on 1984-01-30 with total page 898 pages. Available in PDF, EPUB and Kindle. Book excerpt: Potential theory and certain aspects of probability theory are intimately related, perhaps most obviously in that the transition function determining a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically, a procedure potential theorists observe withjaun diced eyes in view of the fact that now as in the past their subject provides the motivation for much of Markov process theory. However that may be it is clear that certain concepts in potential theory correspond closely to concepts in probability theory, specifically to concepts in martingale theory. For example, superharmonic functions correspond to supermartingales. More specifically: the Fatou type boundary limit theorems in potential theory correspond to supermartingale convergence theorems; the limit properties of monotone sequences of superharmonic functions correspond surprisingly closely to limit properties of monotone sequences of super martingales; certain positive superharmonic functions [supermartingales] are called "potentials," have associated measures in their respective theories and are subject to domination principles (inequalities) involving the supports of those measures; in each theory there is a reduction operation whose properties are the same in the two theories and these reductions induce sweeping (balayage) of the measures associated with potentials, and so on.

Download or read book Potential Theory written by Lester Helms and published by Springer Science & Business Media. This book was released on 2009-05-27 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ?rst six chapters of this book are revised versions of the same chapters in the author’s 1969 book, Introduction to Potential Theory. Atthetimeof the writing of that book, I had access to excellent articles,books, and lecture notes by M. Brelot. The clarity of these works made the task of collating them into a single body much easier. Unfortunately, there is not a similar collection relevant to more recent developments in potential theory. A n- comer to the subject will ?nd the journal literature to be a maze of excellent papers and papers that never should have been published as presented. In the Opinion Column of the August, 2008, issue of the Notices of the Am- ican Mathematical Society, M. Nathanson of Lehman College (CUNY) and (CUNY) Graduate Center said it best “. . . When I read a journal article, I often ?nd mistakes. Whether I can ?x them is irrelevant. The literature is unreliable. ” From time to time, someone must try to ?nd a path through the maze. In planning this book, it became apparent that a de?ciency in the 1969 book would have to be corrected to include a discussion of the Neumann problem, not only in preparation for a discussion of the oblique derivative boundary value problem but also to improve the basic part of the subject matter for the end users, engineers, physicists, etc.

Download or read book Problems in Probability written by Albert N. Shiryaev and published by Springer Science & Business Media. This book was released on 2012-08-07 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the first two editions of the book Probability (GTM 95), each chapter included a comprehensive and diverse set of relevant exercises. While the work on the third edition was still in progress, it was decided that it would be more appropriate to publish a separate book that would comprise all of the exercises from previous editions, in addition to many new exercises. Most of the material in this book consists of exercises created by Shiryaev, collected and compiled over the course of many years while working on many interesting topics. Many of the exercises resulted from discussions that took place during special seminars for graduate and undergraduate students. Many of the exercises included in the book contain helpful hints and other relevant information. Lastly, the author has included an appendix at the end of the book that contains a summary of the main results, notation and terminology from Probability Theory that are used throughout the present book. This Appendix also contains additional material from Combinatorics, Potential Theory and Markov Chains, which is not covered in the book, but is nevertheless needed for many of the exercises included here.

Download or read book Probabilities and Potential written by Claude Dellacherie and published by . This book was released on 1982 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probabilities and Potential B Theory of Martingales written by Claude Dellacherie and published by . This book was released on 1982 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probabilities and Potential C written by Claude Dellacherie and published by . This book was released on 1988 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probabilities and Potential C written by Claude Dellacherie and published by . This book was released on 1988 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Probabilities and Potential written by Claude Dellacherie and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Foundations of Modern Potential Theory written by Naum S. Landkof and published by Springer. This book was released on 2011-11-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a long time potential theory was necessarily viewed as only another chapter of mathematical physics. Developing in close connection with the theory of boundary-value problems for the Laplace operator, it led to the creation of the mathematical apparatus of potentials of single and double layers; this was adequate for treating problems involving smooth boundaries. A. M. Lyapunov is to be credited with the rigorous analysis of the properties of potentials and the possibilities for applying them to the 1 solution of boundary-value problems. The results he obtained at the end of the 19th century later received a more detailed and sharpened exposition in the book by N. M. Gunter, published in Paris in 1934 and 2 in New York 1967 with additions and revisions. Of fundamental significance to potential theory also was the work of H. Poincare, especially his method of sweeping out mass (balayage). At the beginning of the 20th century the work of S. Zaremba and especially of H. Lebesgue attracted the attention of mathematicians to the unsolvable cases of the classical Dirichlet problem. Through the efforts of O. Kellogg, G. Bouligand, and primarily N. Wiener, by the middle of the 20th century the problem of characterizing the so-called irregular points of the boundary of a region (i. e. the points at which the continuity of the solution of the Dirichlet problem may be violated) was completely solved and a procedure to obtain a generalized solution to the Dirichlet problem was described.