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Stochastic Analysis Of Mixed Fractional Gaussian Processes

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Stochastic Analysis of Mixed Fractional Gaussian Processes

Stochastic Analysis of Mixed Fractional Gaussian Processes Book
Author : Yuliya Mishura,Mounir Zili
Publisher : Elsevier
Release : 2018-05-26
ISBN : 0081023634
Language : En, Es, Fr & De

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Book Description :

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

Fractional Brownian Motion

Fractional Brownian Motion Book
Author : Oksana Banna,Yuliya Mishura,Kostiantyn Ralchenko,Sergiy Shklyar
Publisher : John Wiley & Sons
Release : 2019-04-09
ISBN : 1119610346
Language : En, Es, Fr & De

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Book Description :

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.

Modern Problems of Stochastic Analysis and Statistics

Modern Problems of Stochastic Analysis and Statistics Book
Author : Vladimir Panov
Publisher : Springer
Release : 2017-11-21
ISBN : 331965313X
Language : En, Es, Fr & De

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Book Description :

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 stochastic analysis and statistics”, held at the Higher School of Economics in Moscow from May 29 - June 2, 2016. It offers a valuable reference resource for researchers and graduate students interested in modern stochastics.

Stochastic Calculus for Fractional Brownian Motion and Related Processes

Stochastic Calculus for Fractional Brownian Motion and Related Processes Book
Author : Yuliya Mishura
Publisher : Springer
Release : 2008-04-12
ISBN : 3540758739
Language : En, Es, Fr & De

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Book Description :

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 and Infinite Dimensional Analysis

Stochastic and Infinite Dimensional Analysis Book
Author : Christopher C. Bernido,Maria Victoria Carpio-Bernido,Martin Grothaus,Tobias Kuna,Maria João Oliveira,José Luís da Silva
Publisher : Birkhäuser
Release : 2016-08-10
ISBN : 3319072455
Language : En, Es, Fr & De

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Book Description :

This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.

Discrete Time Approximations and Limit Theorems

Discrete Time Approximations and Limit Theorems Book
Author : Yuliya Mishura,Kostiantyn Ralchenko
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2021-10-25
ISBN : 3110652994
Language : En, Es, Fr & De

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Book Description :

Financial market modeling is a prime example of a real-life application of probability theory and stochastics. This authoritative book discusses the discrete-time approximation and other qualitative properties of models of financial markets, like the Black-Scholes model and its generalizations, offering in this way rigorous insights on one of the most interesting applications of mathematics nowadays.

Analysis of Variations for Self similar Processes

Analysis of Variations for Self similar Processes Book
Author : Ciprian Tudor
Publisher : Springer Science & Business Media
Release : 2013-08-13
ISBN : 3319009362
Language : En, Es, Fr & De

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Book Description :

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.

Stochastic Models

Stochastic Models Book
Author : José González-Barrios,Ana Meda
Publisher : American Mathematical Soc.
Release : 2003
ISBN : 0821834665
Language : En, Es, Fr & De

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Book Description :

The volume includes lecture notes and research papers by participants of the Seventh Symposium on Probability and Stochastic Processes held in Mexico City. The lecture notes introduce recent advances in stochastic calculus with respect to fractional Brownian motion, principles of large deviations and of minimum entropy concerning equilibrium prices in random economic systems, and give a complete and thorough survey of credit risk theory. The research papers cover areas such as financial markets, Gaussian processes, stochastic differential equations, stochastic integration, quantum dynamical semigroups, self-intersection local times, etc. Readers should have a basic background in probability theory, stochastic integration, and stochastic differential equations. The book is suitable for graduate students and research mathematicians interested in probability, stochastic processes, and risk theory.

S minaire de Probabilit s XLIII

S  minaire de Probabilit  s XLIII Book
Author : Catherine Donati Martin,Antoine Lejay,Alain Rouault
Publisher : Springer
Release : 2010-10-20
ISBN : 3642152171
Language : En, Es, Fr & De

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Book Description :

This is a new volume of the Séminaire de Probabilités which is now in its 43rd year. Following the tradition, this volume contains about 20 original research and survey articles on topics related to stochastic analysis. It contains an advanced course of J. Picard on the representation formulae for fractional Brownian motion. The regular chapters cover a wide range of themes, such as stochastic calculus and stochastic differential equations, stochastic differential geometry, filtrations, analysis on Wiener space, random matrices and free probability, as well as mathematical finance. Some of the contributions were presented at the Journées de Probabilités held in Poitiers in June 2009.

Parameter Estimation in Fractional Diffusion Models

Parameter Estimation in Fractional Diffusion Models Book
Author : Kęstutis Kubilius,Yuliya Mishura,Kostiantyn Ralchenko
Publisher : Springer
Release : 2018-01-04
ISBN : 3319710303
Language : En, Es, Fr & De

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Book Description :

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,” i.e., uncorrelated. However, many processes in the natural sciences, computer networks and financial markets have long-term or short-term dependences, i.e., the correlations of random noise in these processes are non-zero, and slowly or rapidly decrease with time. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion. Therefore, the book constructs diffusion models with memory and provides simple and suitable parameter estimation methods in these models, making it a valuable resource for all researchers in this field. The book is addressed to specialists and researchers in the theory and statistics of stochastic processes, practitioners who apply statistical methods of parameter estimation, graduate and post-graduate students who study mathematical modeling and statistics.

Mathematical Finance

Mathematical Finance Book
Author : Workshop of the Mathematical Finance Research Project
Publisher : Springer Science & Business Media
Release : 2001-06
ISBN : 9783764365530
Language : En, Es, Fr & De

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Book Description :

The year 2000 is the centenary year of the publication of Bachelier's thesis which - together with Harry Markovitz Ph. D. dissertation on portfolio selection in 1952 and Fischer Black's and Myron Scholes' solution of an option pricing problem in 1973 - is considered as the starting point of modern finance as a mathematical discipline. On this remarkable anniversary the workshop on mathematical finance held at the University of Konstanz brought together practitioners, economists and mathematicians to discuss the state of the art. Apart from contributions to the known discrete, Brownian, and Lvy process models, first attempts to describe a market in a reasonable way by a fractional Brownian motion model are presented, opening many new aspects for practitioners and new problems for mathematicians. As most dynamical financial problems are stochastic filtering or control problems many talks presented adaptations of control methods and techniques to the classical financial problems in portfolio selection irreversible investment risk sensitive asset allocation capital asset pricing hedging contingent claims option pricing interest rate theory. The contributions of practitioners link the theoretical results to the steadily increasing flow of real world problems from financial institutions into mathematical laboratories. The present volume reflects this exchange of theoretical and applied results, methods and techniques that made the workshop a fruitful contribution to the interdisciplinary work in mathematical finance.

Stochastic Processes and Applications

Stochastic Processes and Applications Book
Author : Sergei Silvestrov,Anatoliy Malyarenko,Milica Rančić
Publisher : Springer
Release : 2018-12-05
ISBN : 3030028259
Language : En, Es, Fr & De

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Book Description :

This book highlights the latest advances in stochastic processes, probability theory, mathematical statistics, engineering mathematics and algebraic structures, focusing on mathematical models, structures, concepts, problems and computational methods and algorithms important in modern technology, engineering and natural sciences applications. It comprises selected, high-quality, refereed contributions from various large research communities in modern stochastic processes, algebraic structures and their interplay and applications. The chapters cover both theory and applications, illustrated by numerous figures, schemes, algorithms, tables and research results to help readers understand the material and develop new mathematical methods, concepts and computing applications in the future. Presenting new methods and results, reviews of cutting-edge research, and open problems and directions for future research, the book serves as a source of inspiration for a broad spectrum of researchers and research students in probability theory and mathematical statistics, applied algebraic structures, applied mathematics and other areas of mathematics and applications of mathematics. The book is based on selected contributions presented at the International Conference on “Stochastic Processes and Algebraic Structures – From Theory Towards Applications” (SPAS2017) to mark Professor Dmitrii Silvestrov’s 70th birthday and his 50 years of fruitful service to mathematics, education and international cooperation, which was held at Mälardalen University in Västerås and Stockholm University, Sweden, in October 2017.

Statistical Inference for Fractional Diffusion Processes

Statistical Inference for Fractional Diffusion Processes Book
Author : B. L. S. Prakasa Rao
Publisher : John Wiley & Sons
Release : 2011-07-05
ISBN : 0470975768
Language : En, Es, Fr & De

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Book Description :

Stochastic processes are widely used for model building in the social, physical, engineering and life sciences as well as in financial economics. In model building, statistical inference for stochastic processes is of great importance from both a theoretical and an applications point of view. This book deals with Fractional Diffusion Processes and statistical inference for such stochastic processes. The main focus of the book is to consider parametric and nonparametric inference problems for fractional diffusion processes when a complete path of the process over a finite interval is observable. Key features: Introduces self-similar processes, fractional Brownian motion and stochastic integration with respect to fractional Brownian motion. Provides a comprehensive review of statistical inference for processes driven by fractional Brownian motion for modelling long range dependence. Presents a study of parametric and nonparametric inference problems for the fractional diffusion process. Discusses the fractional Brownian sheet and infinite dimensional fractional Brownian motion. Includes recent results and developments in the area of statistical inference of fractional diffusion processes. Researchers and students working on the statistics of fractional diffusion processes and applied mathematicians and statisticians involved in stochastic process modelling will benefit from this book.

Stochastic Calculus for Fractional Brownian Motion and Applications

Stochastic Calculus for Fractional Brownian Motion and Applications Book
Author : Francesca Biagini,Yaozhong Hu,Bernt Øksendal,Tusheng Zhang
Publisher : Springer Science & Business Media
Release : 2008-02-17
ISBN : 1846287979
Language : En, Es, Fr & De

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Book Description :

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.

Beyond The Triangle Brownian Motion Ito Calculus And Fokker planck Equation Fractional Generalizations

Beyond The Triangle  Brownian Motion  Ito Calculus  And Fokker planck Equation   Fractional Generalizations Book
Author : Sabir Umarov,Marjorie Hahn,Kei Kobayashi
Publisher : World Scientific
Release : 2018-02-13
ISBN : 9813230991
Language : En, Es, Fr & De

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Book Description :

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.

Stochastic Processes with Applications

Stochastic Processes with Applications Book
Author : Antonio Di Crescenzo,Claudio Macci,Barbara Martinucci
Publisher : MDPI
Release : 2019-11-28
ISBN : 3039217283
Language : En, Es, Fr & De

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Book Description :

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 certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included.

Mathematical Reviews

Mathematical Reviews Book
Author : Anonim
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Mathematical Reviews book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Stable Non Gaussian Random Processes

Stable Non Gaussian Random Processes Book
Author : Gennady Samorodnitsky,M.S. Taqqu
Publisher : CRC Press
Release : 1994-06-01
ISBN : 9780412051715
Language : En, Es, Fr & De

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Book Description :

Both an introduction and a basic reference text on non-Gaussian stable models, for graduate students and practitioners. Assuming only a first-year graduate course in probability, it includes material which has only recently appeared in journals and unpublished materials. Each chapter begins with a brief overview and concludes with a range of exercises at varying levels of difficulty. Proofs are spelled out in detail. The volume includes a discussion of self-similar processes, ARMA, and fractional ARIMA time series with stable innovations. Annotation copyright by Book News, Inc., Portland, OR

System Control and Rough Paths

System Control and Rough Paths Book
Author : Terry Lyons,Wallis Professor of Mathematics Terry Lyons,Zhongmin Qian
Publisher : Oxford University Press
Release : 2002
ISBN : 9780198506485
Language : En, Es, Fr & De

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Book Description :

This work describes a completely novel mathematical development which has already influenced probability theory, and has potential for application to engineering and to areas of pure mathematics: the evolution of complex non-linear systems subject to rough or rapidly fluctuating stimuli.

An Introduction to Differential Equations

An Introduction to Differential Equations Book
Author : Anil G Ladde,G S Ladde
Publisher : World Scientific Publishing Company
Release : 2013-01-11
ISBN : 9814397393
Language : En, Es, Fr & De

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Book Description :

Volume 1: Deterministic Modeling, Methods and Analysis For more than half a century, stochastic calculus and stochastic differential equations have played a major role in analyzing the dynamic phenomena in the biological and physical sciences, as well as engineering. The advancement of knowledge in stochastic differential equations is spreading rapidly across the graduate and postgraduate programs in universities around the globe. This will be the first available book that can be used in any undergraduate/graduate stochastic modeling/applied mathematics courses and that can be used by an interdisciplinary researcher with a minimal academic background. An Introduction to Differential Equations: Volume 2 is a stochastic version of Volume 1 (“An Introduction to Differential Equations: Deterministic Modeling, Methods and Analysis”). Both books have a similar design, but naturally, differ by calculi. Again, both volumes use an innovative style in the presentation of the topics, methods and concepts with adequate preparation in deterministic Calculus. Errata Errata (32 KB)