Some Aspects Of Brownian Motion

Author : Marc Yor
Publisher : Birkhäuser
Page : 160 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034889544

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Some Aspects of Brownian Motion by Marc Yor Pdf

The following notes represent approximately the second half of the lectures I gave in the Nachdiplomvorlesung, in ETH, Zurich, between October 1991 and February 1992, together with the contents of six additional lectures I gave in ETH, in November and December 1993. Part I, the elder brother of the present book [Part II], aimed at the computation, as explicitly as possible, of a number of interesting functionals of Brownian motion. It may be natural that Part II, the younger brother, looks more into the main technique with which Part I was "working", namely: martingales and stochastic calculus. As F. Knight writes, in a review article on Part I, in which research on Brownian motion is compared to gold mining: "In the days of P. Levy, and even as late as the theorems of "Ray and Knight" (1963), it was possible for the practiced eye to pick up valuable reward without the aid of much technology . . . Thereafter, however, the rewards are increasingly achieved by the application of high technology". Although one might argue whether this golden age is really foregone, and discuss the "height" of the technology involved, this quotation is closely related to the main motivations of Part II: this technology, which includes stochastic calculus for general discontinuous semi-martingales, enlargement of filtrations, . . .

Author : Roger Mansuy,Marc Yor
Publisher : Springer Science & Business Media
Page : 205 pages
File Size : 51,7 Mb
Release : 2008-09-16
Category : Mathematics
ISBN : 9783540499664

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Aspects of Brownian Motion by Roger Mansuy,Marc Yor Pdf

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.

Author : Ivan Nourdin
Publisher : Springer Science & Business Media
Page : 133 pages
File Size : 53,7 Mb
Release : 2013-01-17
Category : Mathematics
ISBN : 9788847028234

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Selected Aspects of Fractional Brownian Motion by Ivan Nourdin Pdf

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.

Author : T. Hida
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461260301

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Brownian Motion by T. Hida Pdf

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.

Author : Peter Mörters,Yuval Peres
Publisher : Cambridge University Press
Page : 128 pages
File Size : 48,9 Mb
Release : 2010-03-25
Category : Mathematics
ISBN : 9781139486576

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Brownian Motion by Peter Mörters,Yuval Peres Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 42,6 Mb
Release : 1992
Category : Brownian motion processes
ISBN : LCCN:92036583

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Some Aspects of Brownian Motion by Anonim Pdf

Author : Andrei N. Borodin,Paavo Salminen
Publisher : Springer Science & Business Media
Page : 710 pages
File Size : 46,9 Mb
Release : 2015-07-14
Category : Mathematics
ISBN : 3764367059

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Handbook of Brownian Motion - Facts and Formulae by Andrei N. Borodin,Paavo Salminen Pdf

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.

Author : Ioannis Karatzas,Steven Shreve
Publisher : Springer
Page : 490 pages
File Size : 49,7 Mb
Release : 2014-03-27
Category : Mathematics
ISBN : 9781461209492

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Brownian Motion and Stochastic Calculus by Ioannis Karatzas,Steven Shreve Pdf

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.

Author : René L. Schilling,Lothar Partzsch
Publisher : Walter de Gruyter GmbH & Co KG
Page : 424 pages
File Size : 53,8 Mb
Release : 2014-06-18
Category : Mathematics
ISBN : 9783110307306

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Brownian Motion by René L. Schilling,Lothar Partzsch Pdf

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.

Author : Daniel Revuz,Marc Yor
Publisher : Springer Science & Business Media
Page : 608 pages
File Size : 52,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662064009

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Continuous Martingales and Brownian Motion by Daniel Revuz,Marc Yor Pdf

"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.

Author : Anonim
Publisher : Unknown
Page : 144 pages
File Size : 42,8 Mb
Release : 2024-06-30
Category : Brownian motion processes
ISBN : OCLC:700311659

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Some Aspects of Brownian Motion by Anonim Pdf

Author : René L. Schilling
Publisher : Walter de Gruyter GmbH & Co KG
Page : 533 pages
File Size : 53,7 Mb
Release : 2021-09-07
Category : Mathematics
ISBN : 9783110741278

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Brownian Motion by René L. Schilling Pdf

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''.

Author : Ubbo F. Wiersema
Publisher : John Wiley & Sons
Page : 342 pages
File Size : 48,6 Mb
Release : 2008-12-08
Category : Business & Economics
ISBN : 9780470021705

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Brownian Motion Calculus by Ubbo F. Wiersema Pdf

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.

Author : Frank B. Knight
Publisher : American Mathematical Soc.
Page : 220 pages
File Size : 44,8 Mb
Release : 1981
Category : Mathematics
ISBN : 9780821815182

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Essentials of Brownian Motion and Diffusion by Frank B. Knight Pdf

Presents some gratuitous generalities on scientific method as it relates to diffusion theory. This book defines Brownian motion by the characterization of P Levy, and then constructed in three basic ways and these are proved to be equivalent in the appropriate sense.

Author : Mark A. McKibben,Micah Webster
Publisher : Nova Science Publishers
Page : 0 pages
File Size : 55,6 Mb
Release : 2015
Category : Brownian motion processes
ISBN : 1634836820

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Brownian Motion by Mark A. McKibben,Micah Webster Pdf

The fields of study in which random fluctuations arise and cannot be ignored are as disparate and numerous as there are synonyms for the word "noise." In the nearly two centuries following the discovery of what has come to be known as Brownian motion, named in homage to botanist Robert Brown, scientists, engineers, financial analysts, mathematicians, and literary authors have posited theories, created models, and composed literary works which have accounted for environmental noise. This volume offers a glimpse into the ways in which Brownian motion has crept into a myriad of fields of study through fifteen distinct chapters written by mathematicians, physicists, and other scholars. The intent is to especially highlight the vastness of scholarly work that explains various facets of Nature made possible by one scientist's curiosity sparked by observing sporadic movement of specks of pollen under a microscope in a 19th century laboratory.