Brownian Motion And Potential Theory Modern And Classical

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Brownian Motion and Classical Potential Theory

Author : Sidney Port
Publisher : Elsevier
ISBN 13 : 0323159087
Total Pages : 251 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Brownian Motion and Classical Potential Theory by : Sidney Port

Download or read book Brownian Motion and Classical Potential Theory written by Sidney Port and published by Elsevier. This book was released on 2012-12-02 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brownian Motion and Classical Potential Theory is a six-chapter text that discusses the connection between Brownian motion and classical potential theory. The first three chapters of this book highlight the developing properties of Brownian motion with results from potential theory. The subsequent chapters are devoted to the harmonic and superharmonic functions, as well as the Dirichlet problem. These topics are followed by a discussion on the transient potential theory of Green potentials, with an emphasis on the Newtonian potentials, as well as the recurrent potential theory of logarithmic potentials. The last chapters deal with the application of Brownian motion to obtain the main theorems of classical potential theory. This book will be of value to physicists, chemists, and biologists.

Classical and Modern Potential Theory and Applications

Author : K. GowriSankaran
Publisher : Springer Science & Business Media
ISBN 13 : 9401111383
Total Pages : 467 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Classical and Modern Potential Theory and Applications by : K. GowriSankaran

Download or read book Classical and Modern Potential Theory and Applications written by K. GowriSankaran and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Research Workshop, Château de Bonas, France, July 25--31, 1993

Brownian Motion

Author : Peter Mörters
Publisher : Cambridge University Press
ISBN 13 : 1139486578
Total Pages : pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Brownian Motion by : Peter Mörters

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.

Brownian Motion

Author : T. Hida
Publisher : Springer Science & Business Media
ISBN 13 : 1461260302
Total Pages : 340 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Brownian Motion by : T. Hida

Download or read book Brownian Motion written by T. Hida and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following the publication of the Japanese edition of this book, several inter esting developments took place in the area. The author wanted to describe some of these, as well as to offer suggestions concerning future problems which he hoped would stimulate readers working in this field. For these reasons, Chapter 8 was added. Apart from the additional chapter and a few minor changes made by the author, this translation closely follows the text of the original Japanese edition. We would like to thank Professor J. L. Doob for his helpful comments on the English edition. T. Hida T. P. Speed v Preface The physical phenomenon described by Robert Brown was the complex and erratic motion of grains of pollen suspended in a liquid. In the many years which have passed since this description, Brownian motion has become an object of study in pure as well as applied mathematics. Even now many of its important properties are being discovered, and doubtless new and useful aspects remain to be discovered. We are getting a more and more intimate understanding of Brownian motion.

Classical Potential Theory and Its Probabilistic Counterpart

Author : J. L. Doob
Publisher : Springer Science & Business Media
ISBN 13 : 1461252083
Total Pages : 865 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Classical Potential Theory and Its Probabilistic Counterpart by : J. L. Doob

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 2012-12-06 with total page 865 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.

From Classical to Modern Probability

Author : Pierre Picco
Publisher : Birkhäuser
ISBN 13 : 3034880537
Total Pages : 231 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis From Classical to Modern Probability by : Pierre Picco

Download or read book From Classical to Modern Probability written by Pierre Picco and published by Birkhäuser. This book was released on 2012-12-06 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance. Written at graduate level, the lectures touch the latest advances on each subject, ranging from classical probability theory to modern developments. Thus the book will appeal to students, teachers and researchers working in probability theory or related fields.

Foundations of Modern Probability

Author : Olav Kallenberg
Publisher : Springer Science & Business Media
ISBN 13 : 9780387953137
Total Pages : 670 pages
Book Rating : 4.9/5 (531 download)

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Book Synopsis Foundations of Modern Probability by : Olav Kallenberg

Download or read book Foundations of Modern Probability written by Olav Kallenberg and published by Springer Science & Business Media. This book was released on 2002-01-08 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this single volume on the theory of probability has become a highly-praised standard reference for many areas of probability theory. Chapters from the first edition have been revised and corrected, and this edition contains four new chapters. New material covered includes multivariate and ratio ergodic theorems, shift coupling, Palm distributions, Harris recurrence, invariant measures, and strong and weak ergodicity.

Brownian Motion

Author : René L. Schilling
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311037398X
Total Pages : 514 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Brownian Motion by : René L. Schilling

Download or read book Brownian Motion written by René L. Schilling and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-08-22 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Linear Models

Author : William R. Moser
Publisher : Elsevier
ISBN 13 : 0080510299
Total Pages : 244 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Linear Models by : William R. Moser

Download or read book Linear Models written by William R. Moser and published by Elsevier. This book was released on 1996-10-18 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear models, normally presented in a highly theoretical and mathematical style, are brought down to earth in this comprehensive textbook. Linear Models examines the subject from a mean model perspective, defining simple and easy-to-learn rules for building mean models, regression models, mean vectors, covariance matrices and sums of squares matrices for balanced and unbalanced data sets. The author includes both applied and theoretical discussions of the multivariate normal distribution, quadratic forms, maximum likelihood estimation, less than full rank models, and general mixed models. The mean model is used to bring all of these topics together in a coherent presentation of linear model theory. - Provides a versatile format for investigating linear model theory, using the mean model - Uses examples that are familiar to the student: - Design of experiments, analysis of variance, regression, and normal distribution theory - Includes a review of relevant linear algebra concepts - Contains fully worked examples which follow the theorem/proof presentation

Measure and Integral

Author : Konrad Jacobs
Publisher : Academic Press
ISBN 13 : 1483263045
Total Pages : 593 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Measure and Integral by : Konrad Jacobs

Download or read book Measure and Integral written by Konrad Jacobs and published by Academic Press. This book was released on 2014-07-10 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability and Mathematical Statistics: Measure and Integral provides information pertinent to the general mathematical notions and notations. This book discusses how the machinery of ?-extension works and how ?-content is derived from ?-measure. Organized into 16 chapters, this book begins with an overview of the classical Hahn–Banach theorem and introduces the Banach limits in the form of a major exercise. This text then presents the Daniell extension theory for positive ?-measures. Other chapters consider the transform of ?-contents and ?-measures by measurable mappings and kernels. This text is also devoted to a thorough study of the vector lattice of signed contents. This book discusses as well an abstract regularity theory and applied to the standard cases of compact, locally compact, and Polish spaces. The final chapter deals with the rudiments of the Krein–Milman theorem, along with some of their applications. This book is a valuable resource for graduate students.

Identifiability In Stochastic Models

Author : Bozzano G Luisa
Publisher : Academic Press
ISBN 13 : 0128015268
Total Pages : 271 pages
Book Rating : 4.1/5 (28 download)

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Book Synopsis Identifiability In Stochastic Models by : Bozzano G Luisa

Download or read book Identifiability In Stochastic Models written by Bozzano G Luisa and published by Academic Press. This book was released on 2012-09-18 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of identifiability is basic to all statistical methods and data analysis, occurring in such diverse areas as Reliability Theory, Survival Analysis, and Econometrics, where stochastic modeling is widely used. Mathematics dealing with identifiability per se is closely related to the so-called branch of "characterization problems" in Probability Theory. This book brings together relevant material on identifiability as it occurs in these diverse fields.

Quantum Probability

Author : Stanley P. Gudder
Publisher : Academic Press
ISBN 13 : 0080918484
Total Pages : 331 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Quantum Probability by : Stanley P. Gudder

Download or read book Quantum Probability written by Stanley P. Gudder and published by Academic Press. This book was released on 2014-06-28 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum probability is a subtle blend of quantum mechanics and classical probability theory. Its important ideas can be traced to the pioneering work of Richard Feynman in his path integral formalism.Only recently have the concept and ideas of quantum probability been presented in a rigorous axiomatic framework, and this book provides a coherent and comprehensive exposition of this approach. It gives a unified treatment of operational statistics, generalized measure theory and the path integral formalism that can only be found in scattered research articles.The first two chapters survey the necessary background in quantum mechanics and probability theory and therefore the book is fairly self-contained, assuming only an elementary knowledge of linear operators in Hilbert space.

Topics in Probability and Lie Groups: Boundary Theory

Author : John Christopher Taylor
Publisher : American Mathematical Soc.
ISBN 13 : 0821802755
Total Pages : 214 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topics in Probability and Lie Groups: Boundary Theory by : John Christopher Taylor

Download or read book Topics in Probability and Lie Groups: Boundary Theory written by John Christopher Taylor and published by American Mathematical Soc.. This book was released on 2001 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is comprised of two parts: the first contains articles by S. N. Evans, F. Ledrappier, and Figa-Talomanaca. These articles arose from a Centre de Recherches de Mathematiques (CRM) seminar entitiled, ``Topics in Probability on Lie Groups: Boundary Theory''. Evans gives a synthesis of his pre-1992 work on Gaussian measures on vector spaces over a local field. Ledrappier uses the freegroup on $d$ generators as a paradigm for results on the asymptotic properties of random walks and harmonic measures on the Martin boundary. These articles are followed by a case study by Figa-Talamanca using Gelfand pairs to study a diffusion on a compact ultrametric space. The second part of the book is an appendix to the book Compactifications of Symmetric Spaces (Birkhauser) by Y. Guivarc'h and J. C. Taylor. This appendix consists of an article by each author and presents the contents of this book in a more algebraic way. L. Ji and J.-P. Anker simplifies some of their results on the asymptotics of the Green function that were used to compute Martin boundaries. And Taylor gives a self-contained account of Martin boundary theory for manifolds using the theory of second order strictly elliptic partial differential operators.

Encyclopaedia of Mathematics

Author : M. Hazewinkel
Publisher : Springer
ISBN 13 : 1489937978
Total Pages : 927 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Encyclopaedia of Mathematics by : M. Hazewinkel

Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 927 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Second Course in Stochastic Processes

Author : Samuel Karlin
Publisher : Gulf Professional Publishing
ISBN 13 : 9780123986504
Total Pages : 568 pages
Book Rating : 4.9/5 (865 download)

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Book Synopsis A Second Course in Stochastic Processes by : Samuel Karlin

Download or read book A Second Course in Stochastic Processes written by Samuel Karlin and published by Gulf Professional Publishing. This book was released on 1981-05-12 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic methods in markov chains; Ratio theorems of transition probabilities and applications; Sums of independent random variables as a markov chain; Order statistics, poisson processes, and applications; Continuous time markov chains; Diffusion processes; Compouding stochastic processes; Fluctuation theory of partial sums of independent identically distributed random variables; Queueing processes.

Seminar on Stochastic Processes, 1984

Author : Cinlar
Publisher : Springer Science & Business Media
ISBN 13 : 146846745X
Total Pages : 255 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Seminar on Stochastic Processes, 1984 by : Cinlar

Download or read book Seminar on Stochastic Processes, 1984 written by Cinlar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of about half of the papers presented during a three-day seminar on stochastic processes held at Northwestern U- versity, Evanston. The seminar was the fourth of such yearly seminars aimed at bringing together a small group of researchers to discuss their current work in an informal atmosphere. The invited participants in the seminar were B.W. ATKINSON, R.M. BLUMENTHAL, K. BURDZY, D. BURKHOLDER, M. CRANSTON, C. DOLEANS"'DADE, J.L. DOOB, N. FALKNER, P. FITZSIMMONS, J. GLOVER, F. KNIGHT, T. McCONNELL, J.B. MITRO, S. OREY, J. PITMAN, A.O. PITTENGER, Z. POP- STOJANOVIC, P. PROTTER, T. SALISBURY, M. SHARPE, C.T. SHIH, A. SZNITMAN, S.J. TAYLOR, J. WALSH, and R. WILLIAMS. We thank them and the other partiCipants for the lively seminar they created. The seminar was made possible through the partial support of the Air Force Office of Scientific Research via their Grant No. 82-0109 to Northwestern University. E.

Evolution Equations and Their Applications in Physical and Life Sciences

Author : G Lumer
Publisher : CRC Press
ISBN 13 : 1482277484
Total Pages : 530 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Evolution Equations and Their Applications in Physical and Life Sciences by : G Lumer

Download or read book Evolution Equations and Their Applications in Physical and Life Sciences written by G Lumer and published by CRC Press. This book was released on 2019-04-24 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of lectures on linear partial differntial equations and semigroups, nonlinear equations, stochastic evolutionary processes, and evolution problems from physics, engineering and mathematical biology. The contributions come from the 6th International Conference on Evolution Equations and Their Applications in Physica