Stochastic Calculus For Fractional Brownian Motion And Related Processes
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| Author | : Yuliya Mishura |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 411 |
| Release | : 2008-01-02 |
| Genre | : Mathematics |
| ISBN | : 3540758720 |
Download Stochastic Calculus for Fractional Brownian Motion and Related Processes Book in PDF, Epub and Kindle
This volume examines the theory of fractional Brownian motion and other long-memory processes. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. It proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional market.
| Author | : Francesca Biagini |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 331 |
| Release | : 2008-02-17 |
| Genre | : Mathematics |
| ISBN | : 1846287979 |
Download Stochastic Calculus for Fractional Brownian Motion and Applications Book in PDF, Epub and Kindle
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.
| Author | : Yuliya S. Mishura |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2008 |
| Genre | : Distribution (Probability theory) |
| ISBN | : 9788354075875 |
Download Stochastic Calculus for Fractional Brownian Motion and Related Processes Book in PDF, Epub and Kindle
The theory of fractional Brownian motion and other long-memory processes are addressed in this volume. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. Among these are results about Levy characterization of fractional Brownian motion, maximal moment inequalities for Wiener integrals including the values 0
| Author | : Francesca Biagini |
| Publisher | : Springer |
| Total Pages | : 330 |
| Release | : 2009-10-12 |
| Genre | : Mathematics |
| ISBN | : 9781848008939 |
Download Stochastic Calculus for Fractional Brownian Motion and Applications Book in PDF, Epub and Kindle
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.
| Author | : Ivan Nourdin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 133 |
| Release | : 2013-01-17 |
| Genre | : Mathematics |
| ISBN | : 884702823X |
Download Selected Aspects of Fractional Brownian Motion Book in PDF, Epub and Kindle
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 | : Oksana Banna |
| Publisher | : John Wiley & Sons |
| Total Pages | : 288 |
| Release | : 2019-04-30 |
| Genre | : Mathematics |
| ISBN | : 1786302608 |
Download Fractional Brownian Motion Book in PDF, Epub and Kindle
This monograph studies the relationships between fractional Brownian motion (fBm) and other processes of more simple form. In particular, this book solves the problem of the projection of fBm onto the space of Gaussian martingales that can be represented as Wiener integrals with respect to a Wiener process. It is proved that there exists a unique martingale closest to fBm in the uniform integral norm. Numerical results concerning the approximation problem are given. The upper bounds of distances from fBm to the different subspaces of Gaussian martingales are evaluated and the numerical calculations are involved. The approximations of fBm by a uniformly convergent series of Lebesgue integrals, semimartingales and absolutely continuous processes are presented. As auxiliary but interesting results, the bounds from below and from above for the coefficient appearing in the representation of fBm via the Wiener process are established and some new inequalities for Gamma functions, and even for trigonometric functions, are obtained.
| Author | : Yuliya Mishura |
| Publisher | : Elsevier |
| Total Pages | : 212 |
| Release | : 2018-05-26 |
| Genre | : Mathematics |
| ISBN | : 0081023634 |
Download Stochastic Analysis of Mixed Fractional Gaussian Processes Book in PDF, Epub and Kindle
Stochastic Analysis of Mixed Fractional Gaussian Processes presents the main tools necessary to characterize Gaussian processes. The book focuses on the particular case of the linear combination of independent fractional and sub-fractional Brownian motions with different Hurst indices. Stochastic integration with respect to these processes is considered, as is the study of the existence and uniqueness of solutions of related SDE's. Applications in finance and statistics are also explored, with each chapter supplying a number of exercises to illustrate key concepts. Presents both mixed fractional and sub-fractional Brownian motions Provides an accessible description for mixed fractional gaussian processes that is ideal for Master's and PhD students Includes different Hurst indices
| Author | : Joseph L. McCauley |
| Publisher | : Cambridge University Press |
| Total Pages | : 219 |
| Release | : 2013-02-21 |
| Genre | : Business & Economics |
| ISBN | : 0521763401 |
Download Stochastic Calculus and Differential Equations for Physics and Finance Book in PDF, Epub and Kindle
Provides graduate students and practitioners in physics and economics with a better understanding of stochastic processes.
| Author | : Ciprian Tudor |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 272 |
| Release | : 2013-08-13 |
| Genre | : Mathematics |
| ISBN | : 3319009362 |
Download Analysis of Variations for Self-similar Processes Book in PDF, Epub and Kindle
Self-similar processes are stochastic processes that are invariant in distribution under suitable time scaling, and are a subject intensively studied in the last few decades. This book presents the basic properties of these processes and focuses on the study of their variation using stochastic analysis. While self-similar processes, and especially fractional Brownian motion, have been discussed in several books, some new classes have recently emerged in the scientific literature. Some of them are extensions of fractional Brownian motion (bifractional Brownian motion, subtractional Brownian motion, Hermite processes), while others are solutions to the partial differential equations driven by fractional noises. In this monograph the author discusses the basic properties of these new classes of self-similar processes and their interrelationship. At the same time a new approach (based on stochastic calculus, especially Malliavin calculus) to studying the behavior of the variations of self-similar processes has been developed over the last decade. This work surveys these recent techniques and findings on limit theorems and Malliavin calculus.
| Author | : Jean-François Le Gall |
| Publisher | : Springer |
| Total Pages | : 282 |
| Release | : 2016-04-28 |
| Genre | : Mathematics |
| ISBN | : 3319310895 |
Download Brownian Motion, Martingales, and Stochastic Calculus Book in PDF, Epub and Kindle
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.
