Brownian Brownian Motion I
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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.
Handbook Of Brownian Motion Facts And Formulae
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Author : Andrei N. Borodin
language : en
Publisher: Springer Science & Business Media
Release Date : 2015-07-14
Handbook Of Brownian Motion Facts And Formulae written by Andrei N. Borodin 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 2015-07-14 with Mathematics categories.
Here is easy reference to a wealth of facts and formulae associated with Brownian motion, collecting in one volume more than 2500 numbered formulae. The book serves as a basic reference for researchers, graduate students, and people doing applied work with Brownian motion and diffusions, and can be used as a source of explicit examples when teaching stochastic processes.
From Brownian Motion To Schr Dinger S Equation
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Author : Kai L. Chung
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
From Brownian Motion To Schr Dinger S Equation written by Kai L. 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 2012-12-06 with Mathematics categories.
In recent years, the study of the theory of Brownian motion has become a powerful tool in the solution of problems in mathematical physics. This self-contained and readable exposition by leading authors, provides a rigorous account of the subject, emphasizing the "explicit" rather than the "concise" where necessary, and addressed to readers interested in probability theory as applied to analysis and mathematical physics. A distinctive feature of the methods used is the ubiquitous appearance of stopping time. The book contains much original research by the authors (some of which published here for the first time) as well as detailed and improved versions of relevant important results by other authors, not easily accessible in existing literature.
Brownian Motion And Stochastic Calculus
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Author : Ioannis Karatzas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Brownian Motion And Stochastic Calculus written by Ioannis Karatzas 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.
Two of the most fundamental concepts in the theory of stochastic processes are the Markov property and the martingale property. * This book is written for readers who are acquainted with both of these ideas in the discrete-time setting, and who now wish to explore stochastic processes in their continuous time context. It has been our goal to write a systematic and thorough exposi tion of this subject, leading in many instances to the frontiers of knowledge. At the same time, we have endeavored to keep the mathematical prerequisites as low as possible, namely, knowledge of measure-theoretic probability and some familiarity with discrete-time processes. The vehicle we have chosen for this task is Brownian motion, which we present as the canonical example of both a Markov process and a martingale. We support this point of view by showing how, by means of stochastic integration and random time change, all continuous-path martingales and a multitude of continuous-path Markov processes can be represented in terms of Brownian motion. This approach forces us to leave aside those processes which do not have continuous paths. Thus, the Poisson process is not a primary object of study, although it is developed in Chapter 1 to be used as a tool when we later study passage times and local time of Brownian motion.
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 : Robert M. Mazo
language : en
Publisher: OUP Oxford
Release Date : 2008-10-23
Brownian Motion written by Robert M. Mazo and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-23 with Science categories.
Brownian motion- the incessant motion of small particles suspended in a fluid- is an important topic in statistical physics and physical chemistry. This book studies its origin in molecular scale fluctuations, its description in terms of random process theory and also in terms of statistical mechanics.
Continuous Martingales And Brownian Motion
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Author : Daniel Revuz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Continuous Martingales And Brownian Motion written by Daniel Revuz 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 2013-03-09 with Mathematics categories.
From the reviews: "This is a magnificent book! Its purpose is to describe in considerable detail a variety of techniques used by probabilists in the investigation of problems concerning Brownian motion. The great strength of Revuz and Yor is the enormous variety of calculations carried out both in the main text and also (by implication) in the exercises. ... This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises, and throwing out challenging remarks about areas awaiting further research..." Bull.L.M.S. 24, 4 (1992) Since the first edition in 1991, an impressive variety of advances has been made in relation to the material of this book, and these are reflected in the successive editions.
Stochastic Calculus For Fractional Brownian Motion And Applications
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Author : Francesca Biagini
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-17
Stochastic Calculus For Fractional Brownian Motion And Applications written by Francesca Biagini 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 2008-02-17 with Mathematics categories.
Fractional Brownian motion (fBm) has been widely used to model a number of phenomena in diverse fields from biology to finance. This huge range of potential applications makes fBm an interesting object of study. Several approaches have been used to develop the concept of stochastic calculus for fBm. The purpose of this book is to present a comprehensive account of the different definitions of stochastic integration for fBm, and to give applications of the resulting theory. Particular emphasis is placed on studying the relations between the different approaches. Readers are assumed to be familiar with probability theory and stochastic analysis, although the mathematical techniques used in the book are thoroughly exposed and some of the necessary prerequisites, such as classical white noise theory and fractional calculus, are recalled in the appendices. This book will be a valuable reference for graduate students and researchers in mathematics, biology, meteorology, physics, engineering and finance.
Brownian Motion
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Author : René L. Schilling
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-06-18
Brownian Motion written by René L. Schilling and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-18 with Mathematics categories.
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.
Markov Processes Brownian Motion And Time Symmetry
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Author : Kai Lai Chung
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-07-15
Markov Processes Brownian Motion And Time Symmetry 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 2005-07-15 with Mathematics categories.
From the reviews of the First Edition: "This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester course given by the author at the ETH, Zürich, in the spring of 1970. The author's aim was to present some of the best features of Markov processes and, in particular, of Brownian motion with a minimum of prerequisites and technicalities. The reader who becomes acquainted with the volume cannot but agree with the reviewer that the author was very successful in accomplishing this goal...The volume is very useful for people who wish to learn Markov processes but it seems to the reviewer that it is also of great interest to specialists in this area who could derive much stimulus from it. One can be convinced that it will receive wide circulation." (Mathematical Reviews) This new edition contains 9 new chapters which include new exercises, references, and multiple corrections throughout the original text.