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Stochastic Analysis of Mixed Fractional Gaussian Processes

Stochastic Analysis of Mixed Fractional Gaussian Processes
  • Author : Yuliya Mishura
  • Publsiher : Elsevier
  • Release : 26 May 2018
  • ISBN : 0081023634
  • Pages : 210 pages
  • Rating : 4/5 from 21 ratings
GET THIS BOOKStochastic Analysis of Mixed Fractional Gaussian Processes

Summary:
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


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

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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

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Discrete-Time Approximations and Limit Theorems

Discrete-Time Approximations and Limit Theorems
  • Author : Yuliya Mishura,Kostiantyn Ralchenko
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release : 25 October 2021
GET THIS BOOKDiscrete-Time Approximations and Limit Theorems

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.

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Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems

Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems
  • Author : Yeliz Karaca,Dumitru Baleanu,Yu-Dong Zhang,Osvaldo Gervasi,Majaz Moonis
  • Publisher : Academic Press
  • Release : 01 July 2022
GET THIS BOOKMulti-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems

Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical simulations, case studies as well as applications including theoretical aspects of complexity. Foregrounding Multi-chaos, Fractal and Multi-fractional in the era of Artificial Intelligence (AI), the edited book deals with multi- chaos, fractal, multifractional, fractional calculus, fractional operators, quantum, wavelet, entropy-based applications, artificial intelligence,

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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

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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

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Stochastic and Infinite Dimensional Analysis

Stochastic and Infinite Dimensional Analysis
  • Author : Christopher C. Bernido,Maria Victoria Carpio-Bernido,Martin Grothaus,Tobias Kuna,Maria João Oliveira,José Luís da Silva
  • Publisher : Birkhäuser
  • Release : 10 August 2016
GET THIS BOOKStochastic and Infinite Dimensional Analysis

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

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Stochastic Processes and Applications

Stochastic Processes and Applications
  • Author : Sergei Silvestrov,Anatoliy Malyarenko,Milica Rančić
  • Publisher : Springer
  • Release : 05 December 2018
GET THIS BOOKStochastic Processes and Applications

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

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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,”

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Séminaire de Probabilités XLIII

Séminaire de Probabilités XLIII
  • Author : Catherine Donati Martin,Antoine Lejay,Alain Rouault
  • Publisher : Springer
  • Release : 20 October 2010
GET THIS BOOKSéminaire de Probabilités XLIII

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

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Stochastic Models

Stochastic Models
  • Author : José González-Barrios,Ana Meda
  • Publisher : American Mathematical Soc.
  • Release : 28 June 2022
GET THIS BOOKStochastic Models

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,

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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

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Statistical Inference for Fractional Diffusion Processes

Statistical Inference for Fractional Diffusion Processes
  • Author : B. L. S. Prakasa Rao
  • Publisher : John Wiley & Sons
  • Release : 05 July 2011
GET THIS BOOKStatistical Inference for Fractional Diffusion Processes

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

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Stochastic Calculus for Fractional Brownian Motion and Related Processes

Stochastic Calculus for Fractional Brownian Motion and Related Processes
  • Author : Yuliya Mishura
  • Publisher : Springer
  • Release : 12 April 2008
GET THIS BOOKStochastic Calculus for Fractional Brownian Motion and Related Processes

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.

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