Stochastic Analysis of Mixed Fractional Gaussian Processes

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

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  • Author : Yuliya Mishura
  • Publisher : Elsevier
  • Pages : 210 pages
  • ISBN : 0081023634
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKStochastic Analysis of Mixed Fractional Gaussian Processes

Stochastic Analysis of Mixed Fractional Gaussian Processes

Stochastic Analysis of Mixed Fractional Gaussian Processes
  • Author : Yuliya Mishura,Mounir Zili
  • Publisher : Elsevier
  • Release : 26 May 2018
GET THIS BOOKStochastic Analysis of Mixed Fractional Gaussian Processes

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

Stochastic Calculus for Fractional Brownian Motion and Related Processes

Stochastic Calculus for Fractional Brownian Motion and Related Processes
  • Author : IUliia S. Mishura,I︠U︡lii︠a︡ S. Mishura,Yuliya Mishura,Julija S. Mišura,Ûliâ Stepanovna Mišura
  • Publisher : Springer Science & Business Media
  • Release : 02 January 2008
GET THIS BOOKStochastic Calculus for Fractional Brownian Motion and Related Processes

This volume grew out of a series of preprints which were written and circulated - tween 1993 and 1994. Around the same time, related work was done independently by Harder 40] and Laumon 62]. In writing this text based on a revised version of these preprints that were widely distributed in summer 1995, I ?nally did not p- sue the original plan to completely reorganize the original preprints. After the long delay, one of the reasons was that an overview of the results is now

Fractional Brownian Motion

Fractional Brownian Motion
  • Author : Oksana Banna,Yuliya Mishura,Kostiantyn Ralchenko,Sergiy Shklyar
  • Publisher : John Wiley & Sons
  • Release : 09 April 2019
GET THIS BOOKFractional Brownian Motion

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

Modern Problems of Stochastic Analysis and Statistics

Modern Problems of Stochastic Analysis and Statistics
  • Author : Vladimir Panov
  • Publisher : Springer
  • Release : 21 November 2017
GET THIS BOOKModern Problems of Stochastic Analysis and Statistics

This book brings together the latest findings in the area of stochastic analysis and statistics. The individual chapters cover a wide range of topics from limit theorems, Markov processes, nonparametric methods, acturial science, population dynamics, and many others. The volume is dedicated to Valentin Konakov, head of the International Laboratory of Stochastic Analysis and its Applications on the occasion of his 70th birthday. Contributions were prepared by the participants of the international conference of the international conference “Modern problems of

Analysis of Variations for Self-similar Processes

Analysis of Variations for Self-similar Processes
  • Author : Ciprian Tudor
  • Publisher : Springer Science & Business Media
  • Release : 13 August 2013
GET THIS BOOKAnalysis of Variations for Self-similar Processes

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

Parameter Estimation in Fractional Diffusion Models

Parameter Estimation in Fractional Diffusion Models
  • Author : Kęstutis Kubilius,Yuliya Mishura,Kostiantyn Ralchenko
  • Publisher : Springer
  • Release : 04 January 2018
GET THIS BOOKParameter Estimation in Fractional Diffusion Models

This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. For many years now, standard Brownian motion has been (and still remains) a popular model of randomness used to investigate processes in the natural sciences, financial markets, and the economy. The substantial limitation in the use of stochastic diffusion models with Brownian motion is due to the fact that the motion has independent increments, and, therefore, the random noise it generates is “white,”

Markov Processes, Gaussian Processes, and Local Times

Markov Processes, Gaussian Processes, and Local Times
  • Author : Michael B. Marcus,Jay Rosen
  • Publisher : Cambridge University Press
  • Release : 24 July 2006
GET THIS BOOKMarkov Processes, Gaussian Processes, and Local Times

This book was first published in 2006. Written by two of the foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and experts in related fields. The book starts by developing the

Selected Aspects of Fractional Brownian Motion

Selected Aspects of Fractional Brownian Motion
  • Author : Ivan Nourdin
  • Publisher : Springer Science & Business Media
  • Release : 17 January 2013
GET THIS BOOKSelected Aspects of Fractional Brownian Motion

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

Stochastic Analysis and Applications to Finance

Stochastic Analysis and Applications to Finance
  • Author : Tusheng Zhang
  • Publisher : World Scientific
  • Release : 25 January 2021
GET THIS BOOKStochastic Analysis and Applications to Finance

This volume is a collection of solicited and refereed articles from distinguished researchers across the field of stochastic analysis and its application to finance. The articles represent new directions and newest developments in this exciting and fast growing area. The covered topics range from Markov processes, backward stochastic differential equations, stochastic partial differential equations, stochastic control, potential theory, functional inequalities, optimal stopping, portfolio selection, to risk measure and risk theory. It will be a very useful book for young researchers

Stochastic Calculus for Fractional Brownian Motion and Applications

Stochastic Calculus for Fractional Brownian Motion and Applications
  • Author : Francesca Biagini,Yaozhong Hu,Bernt Øksendal,Tusheng Zhang
  • Publisher : Springer Science & Business Media
  • Release : 17 February 2008
GET THIS BOOKStochastic Calculus for Fractional Brownian Motion and Applications

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

Fractional Calculus and Fractional Processes with Applications to Financial Economics

Fractional Calculus and Fractional Processes with Applications to Financial Economics
  • Author : Hasan Fallahgoul,Sergio Focardi,Frank Fabozzi
  • Publisher : Academic Press
  • Release : 06 October 2016
GET THIS BOOKFractional Calculus and Fractional Processes with Applications to Financial Economics

Fractional Calculus and Fractional Processes with Applications to Financial Economics presents the theory and application of fractional calculus and fractional processes to financial data. Fractional calculus dates back to 1695 when Gottfried Wilhelm Leibniz first suggested the possibility of fractional derivatives. Research on fractional calculus started in full earnest in the second half of the twentieth century. The fractional paradigm applies not only to calculus, but also to stochastic processes, used in many applications in financial economics such as modelling volatility,

Stochastic Processes with Applications

Stochastic Processes with Applications
  • Author : Antonio Di Crescenzo,Claudio Macci,Barbara Martinucci
  • Publisher : MDPI
  • Release : 28 November 2019
GET THIS BOOKStochastic Processes with Applications

Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines. This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas