Stochastic Calculus for Fractional Brownian Motion and Applications
Title | Stochastic Calculus for Fractional Brownian Motion and Applications PDF eBook |
Author | Francesca Biagini |
Publisher | Springer Science & Business Media |
Pages | 331 |
Release | 2008-02-17 |
Genre | Mathematics |
ISBN | 1846287979 |
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 Applications
Title | Stochastic Calculus for Fractional Brownian Motion and Applications PDF eBook |
Author | Francesca Biagini |
Publisher | Springer |
Pages | 330 |
Release | 2009-10-12 |
Genre | Mathematics |
ISBN | 9781848008939 |
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
Title | Stochastic Calculus for Fractional Brownian Motion and Related Processes PDF eBook |
Author | Yuliya Mishura |
Publisher | Springer Science & Business Media |
Pages | 411 |
Release | 2008-01-02 |
Genre | Mathematics |
ISBN | 3540758720 |
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 with Fractional Brownian Motion
Title | Stochastic Calculus with Fractional Brownian Motion PDF eBook |
Author | Anastasia A. Ruzmaikina |
Publisher | |
Pages | 112 |
Release | 1999 |
Genre | |
ISBN |
Introduction to Stochastic Calculus with Applications
Title | Introduction to Stochastic Calculus with Applications PDF eBook |
Author | Fima C. Klebaner |
Publisher | Imperial College Press |
Pages | 431 |
Release | 2005 |
Genre | Mathematics |
ISBN | 1860945554 |
This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.
Introduction To Stochastic Calculus With Applications (2nd Edition)
Title | Introduction To Stochastic Calculus With Applications (2nd Edition) PDF eBook |
Author | Fima C Klebaner |
Publisher | World Scientific Publishing Company |
Pages | 431 |
Release | 2005-06-20 |
Genre | Mathematics |
ISBN | 1848168225 |
This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author./a
Stochastic Analysis of Mixed Fractional Gaussian Processes
Title | Stochastic Analysis of Mixed Fractional Gaussian Processes PDF eBook |
Author | Yuliya Mishura |
Publisher | Elsevier |
Pages | 212 |
Release | 2018-05-26 |
Genre | Mathematics |
ISBN | 0081023634 |
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