Stochastic Calculus For Fractional Brownian Motion And Related Processes
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Stochastic Calculus For Fractional Brownian Motion And Related Processes
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Author : Yuliya Mishura
language : en
Publisher: Springer
Release Date : 2008-04-12
Stochastic Calculus For Fractional Brownian Motion And Related Processes written by Yuliya Mishura and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-12 with Mathematics categories.
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.
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.
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.
Stochastic Calculus For Fractional Brownian Motion And Related Processes
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Author : Yuliya Mishura
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-02
Stochastic Calculus For Fractional Brownian Motion And Related Processes written by Yuliya Mishura 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 2008-01-02 with Mathematics categories.
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.
Stochastic Calculus For Fractional Brownian Motion And Applications
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Author : Francesca Biagini
language : en
Publisher: Springer
Release Date : 2009-10-12
Stochastic Calculus For Fractional Brownian Motion And Applications written by Francesca Biagini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-12 with Mathematics categories.
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.
Analysis Of Variations For Self Similar Processes
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Author : Ciprian Tudor
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-13
Analysis Of Variations For Self Similar Processes written by Ciprian Tudor 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 2013-08-13 with Mathematics categories.
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.
Integral Transformations And Anticipative Calculus For Fractional Brownian Motions
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Author : Yaozhong Hu
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Integral Transformations And Anticipative Calculus For Fractional Brownian Motions written by Yaozhong Hu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Fractional calculus categories.
A paper that studies two types of integral transformation associated with fractional Brownian motion. They are applied to construct approximation schemes for fractional Brownian motion by polygonal approximation of standard Brownian motion. This approximation is the best in the sense that it minimizes the mean square error.
Beyond The Triangle Brownian Motion Ito Calculus And Fokker Planck Equation Fractional Generalizations
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Author : Sabir Umarov
language : en
Publisher: World Scientific
Release Date : 2018-02-13
Beyond The Triangle Brownian Motion Ito Calculus And Fokker Planck Equation Fractional Generalizations written by Sabir Umarov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-13 with Mathematics categories.
The book is devoted to the fundamental relationship between three objects: a stochastic process, stochastic differential equations driven by that process and their associated Fokker-Planck-Kolmogorov equations. This book discusses wide fractional generalizations of this fundamental triple relationship, where the driving process represents a time-changed stochastic process; the Fokker-Planck-Kolmogorov equation involves time-fractional order derivatives and spatial pseudo-differential operators; and the associated stochastic differential equation describes the stochastic behavior of the solution process. It contains recent results obtained in this direction.This book is important since the latest developments in the field, including the role of driving processes and their scaling limits, the forms of corresponding stochastic differential equations, and associated FPK equations, are systematically presented. Examples and important applications to various scientific, engineering, and economics problems make the book attractive for all interested researchers, educators, and graduate students.
Analysis Of Variations For Self Similar Processes
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Author : Ciprian A. Tudor
language : en
Publisher: Springer
Release Date : 2013-08-08
Analysis Of Variations For Self Similar Processes written by Ciprian A. Tudor and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-08 with Mathematics categories.
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.
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.
Selected Aspects Of Fractional Brownian Motion
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Author : Ivan Nourdin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-17
Selected Aspects Of Fractional Brownian Motion written by Ivan Nourdin 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 2013-01-17 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.