Some Aspects Of Brownian Motion

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Some Aspects Of Brownian Motion

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Author : Marc Yor
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Some Aspects Of Brownian Motion written by Marc Yor and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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, . . .

Aspects Of Brownian Motion

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Author : Roger Mansuy
language : en
Publisher: Springer
Release Date : 2008-09-16

Aspects Of Brownian Motion written by Roger Mansuy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-16 with Mathematics categories.

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.

Some Aspects Of Brownian Motion

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Author : Marc Yor
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-03-20

Some Aspects Of Brownian Motion written by Marc Yor 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 1997-03-20 with Mathematics categories.

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, . . .

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.

Selected Aspects Of Fractional Brownian Motion

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Author : Ivan Nourdin
language : en
Publisher: Springer
Release Date : 2012-10-17

Selected Aspects Of Fractional Brownian Motion written by Ivan Nourdin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-17 with Mathematics categories.

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.

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.

Some Aspects Of Brownian Motion

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Author :
language : en
Publisher:
Release Date : 1992

Some Aspects Of Brownian Motion written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Brownian motion processes categories.

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.

Computation And Applied Mathematics

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Author :
language : en
Publisher:
Release Date : 1997

Computation And Applied Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.

Brownian Motion And Stochastic Calculus

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Author : Ioannis Karatzas
language : en
Publisher: Springer
Release Date : 2014-03-27

Brownian Motion And Stochastic Calculus written by Ioannis Karatzas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-27 with Mathematics categories.

This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish 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. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This 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 text is complemented by a large number of problems and exercises.