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The Brownian Motion
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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.
Book Synopsis The Brownian Motion by : Andreas Löffler
Download or read book The Brownian Motion written by Andreas Löffler and published by Springer. This book was released on 2019-07-03 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook is the first to provide Business and Economics Ph.D. students with a precise and intuitive introduction to the formal backgrounds of modern financial theory. It explains Brownian motion, random processes, measures, and Lebesgue integrals intuitively, but without sacrificing the necessary mathematical formalism, making them accessible for readers with little or no previous knowledge of the field. It also includes mathematical definitions and the hidden stories behind the terms discussing why the theories are presented in specific ways.
Book Synopsis Handbook of Brownian Motion - Facts and Formulae by : Andrei N. Borodin
Download or read book Handbook of Brownian Motion - Facts and Formulae written by Andrei N. Borodin and published by Springer Science & Business Media. This book was released on 2015-07-14 with total page 710 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Brownian Motion Calculus by : Ubbo F. Wiersema
Download or read book Brownian Motion Calculus written by Ubbo F. Wiersema and published by John Wiley & Sons. This book was released on 2008-12-08 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: BROWNIAN MOTION CALCULUS Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. The sequence of chapters starts with a description of Brownian motion, the random process which serves as the basic driver of the irregular behaviour of financial quantities. That exposition is based on the easily understood discrete random walk. Thereafter the gains from trading in a random environment are formulated in a discrete-time setting. The continuous-time equivalent requires a new concept, the Itō stochastic integral. Its construction is explained step by step, using the so-called norm of a random process (its magnitude), of which a motivated exposition is given in an Annex. The next topic is Itō’s formula for evaluating stochastic integrals; it is the random process counter part of the well known Taylor formula for functions in ordinary calculus. Many examples are given. These ingredients are then used to formulate some well established models for the evolution of stock prices and interest rates, so-called stochastic differential equations, together with their solution methods. Once all that is in place, two methodologies for option valuation are presented. One uses the concept of a change of probability and the Girsanov transformation, which is at the core of financial mathematics. As this technique is often perceived as a magic trick, particular care has been taken to make the explanation elementary and to show numerous applications. The final chapter discusses how computations can be made more convenient by a suitable choice of the so-called numeraire. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website www.wiley.com/go/brownianmotioncalculus.
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.
Book Synopsis Brownian Motion, Obstacles and Random Media by : Alain-Sol Sznitman
Download or read book Brownian Motion, Obstacles and Random Media written by Alain-Sol Sznitman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an account for the non-specialist of the circle of ideas, results and techniques, which grew out in the study of Brownian motion and random obstacles. It also includes an overview of known results and connections with other areas of random media, taking a highly original and personal approach throughout.
Book Synopsis Brownian Motion and Stochastic Calculus by : Ioannis Karatzas
Download or read book Brownian Motion and Stochastic Calculus written by Ioannis Karatzas and published by Springer. This book was released on 2014-03-27 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.
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 2014-06-18 with total page 424 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.
Book Synopsis Aspects of Brownian Motion by : Roger Mansuy
Download or read book Aspects of Brownian Motion written by Roger Mansuy and published by Springer Science & Business Media. This book was released on 2008-09-16 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic calculus and excursion theory are very efficient tools for obtaining either exact or asymptotic results about Brownian motion and related processes. This book focuses on special classes of Brownian functionals, including Gaussian subspaces of the Gaussian space of Brownian motion; Brownian quadratic funtionals; Brownian local times; Exponential functionals of Brownian motion with drift; Time spent by Brownian motion below a multiple of its one-sided supremum.
Book Synopsis Continuous Martingales and Brownian Motion by : Daniel Revuz
Download or read book Continuous Martingales and Brownian Motion written by Daniel Revuz and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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....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." –BULLETIN OF THE L.M.S.
Book Synopsis Selected Aspects of Fractional Brownian Motion by : Ivan Nourdin
Download or read book Selected Aspects of Fractional Brownian Motion written by Ivan Nourdin and published by Springer Science & Business Media. This book was released on 2013-01-17 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional Brownian motion (fBm) is a stochastic process which deviates significantly from Brownian motion and semimartingales, and others classically used in probability theory. As a centered Gaussian process, it is characterized by the stationarity of its increments and a medium- or long-memory property which is in sharp contrast with martingales and Markov processes. FBm has become a popular choice for applications where classical processes cannot model these non-trivial properties; for instance long memory, which is also known as persistence, is of fundamental importance for financial data and in internet traffic. The mathematical theory of fBm is currently being developed vigorously by a number of stochastic analysts, in various directions, using complementary and sometimes competing tools. This book is concerned with several aspects of fBm, including the stochastic integration with respect to it, the study of its supremum and its appearance as limit of partial sums involving stationary sequences, to name but a few. The book is addressed to researchers and graduate students in probability and mathematical statistics. With very few exceptions (where precise references are given), every stated result is proved.
Book Synopsis Brownian Motion and Diffusion by : David Freedman
Download or read book Brownian Motion and Diffusion written by David Freedman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: A long time ago I started writing a book about Markov chains, Brownian motion, and diffusion. I soon had two hundred pages of manuscript and my publisher was enthusiastic. Some years and several drafts later, I had a thot:sand pages of manuscript, and my publisher was less enthusiastic. So we made it a trilogy: Markov Chains Brownian Motion and Diffusion Approximating Countable Markov Chains familiarly - Me, B & D, and ACM. I wrote the first two books for beginning graduate students with some knowledge of probability; if you can follow Sections 3.4 to 3.9 of Brownian Motion and Diffusion you're in. The first two books are quite independent of one another, and completely independent of the third. This last book is a monograph, which explains one way to think about chains with instantaneous states. The results in it are supposed to be new, except where there are spe cific disclaimers; it's written in the framework of Markov Chains. Most of the proofs in the trilogy are new, and I tried hard to make them explicit. The old ones were often elegant, but I seldom saw what made them go. With my own, I can sometimes show you why things work. And, as I will argue in a minute, my demonstrations are easier technically. If I wrote them down well enough, you may come to agree.
Download or read book Brownian Motion written by Robert M. Mazo and published by Oxford University Press on Demand. This book was released on 2002 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. - ;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 statistica.
Book Synopsis Investigations on the Theory of the Brownian Movement by : Albert Einstein
Download or read book Investigations on the Theory of the Brownian Movement written by Albert Einstein and published by Courier Corporation. This book was released on 1956-01-01 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Five early papers evolve theory that won Einstein a Nobel Prize: "Movement of Small Particles Suspended in a Stationary Liquid Demanded by the Molecular-Kinetic Theory of Heat"; "On the Theory of the Brownian Movement"; "A New Determination of Molecular Dimensions"; "Theoretical Observations on the Brownian Motion"; and "Elementary Theory of the Brownian Motion."
Book Synopsis Brownian Motion and Molecular Reality by : Raghav Seth
Download or read book Brownian Motion and Molecular Reality written by Raghav Seth and published by . This book was released on 2020 with total page 469 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.
Book Synopsis Essentials of Brownian Motion and Diffusion by : Frank B. Knight
Download or read book Essentials of Brownian Motion and Diffusion written by Frank B. Knight and published by American Mathematical Soc.. This book was released on 1981 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to develop the topic of what is loosely called Brownian motion and diffusion theory in such a way as to make the fundamentals accessible to a nonspecialist in the field and to provide a sound basic grasp of the subject without going into the most refined of the technicalities. The intent has been to select and emphasize those results which either have an immediate observational meaning or which seem to contribute most to a general understanding of the subject. The first part of the book presents general properties of the Brownian motion, including the definition, probabilistic and analytic properties, general Markov methods, generalizations, and applications. The second part contains the study of local times (in particular, the Trotter theorem) and various types of boundary conditions for Brownian motion.
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 2021-09-07 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itô Integrals'' and ''Brownian Local Times''.
