Parameter Estimation In Fractional Diffusion Models

Author : Kęstutis Kubilius,Yuliya Mishura,Kostiantyn Ralchenko
Publisher : Springer
Page : 390 pages
File Size : 55,9 Mb
Release : 2018-01-04
Category : Mathematics
ISBN : 9783319710303

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Parameter Estimation in Fractional Diffusion Models by Kęstutis Kubilius,Yuliya Mishura,Kostiantyn Ralchenko Pdf

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.

Author : Jaya P. N. Bishwal
Publisher : Springer
Page : 268 pages
File Size : 54,7 Mb
Release : 2007-09-26
Category : Mathematics
ISBN : 9783540744481

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Parameter Estimation in Stochastic Differential Equations by Jaya P. N. Bishwal Pdf

Parameter estimation in stochastic differential equations and stochastic partial differential equations is the science, art and technology of modeling complex phenomena. The subject has attracted researchers from several areas of mathematics. This volume presents the estimation of the unknown parameters in the corresponding continuous models based on continuous and discrete observations and examines extensively maximum likelihood, minimum contrast and Bayesian methods.

Author : Jaya P. N. Bishwal
Publisher : Springer Nature
Page : 634 pages
File Size : 46,8 Mb
Release : 2022-08-06
Category : Mathematics
ISBN : 9783031038617

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Parameter Estimation in Stochastic Volatility Models by Jaya P. N. Bishwal Pdf

This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.

Author : B. L. S. Prakasa Rao
Publisher : John Wiley & Sons
Page : 213 pages
File Size : 49,5 Mb
Release : 2011-07-05
Category : Mathematics
ISBN : 9780470975763

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Statistical Inference for Fractional Diffusion Processes by B. L. S. Prakasa Rao Pdf

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.

Author : Sergei Silvestrov,Anatoliy Malyarenko,Milica Rančić
Publisher : Springer
Page : 475 pages
File Size : 41,8 Mb
Release : 2018-12-05
Category : Mathematics
ISBN : 9783030028251

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Stochastic Processes and Applications by Sergei Silvestrov,Anatoliy Malyarenko,Milica Rančić Pdf

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.

Author : Yuliya Mishura,Mounir Zili
Publisher : Elsevier
Page : 210 pages
File Size : 46,8 Mb
Release : 2018-05-26
Category : Mathematics
ISBN : 9780081023631

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Stochastic Analysis of Mixed Fractional Gaussian Processes by Yuliya Mishura,Mounir Zili Pdf

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

Author : Corinne Berzin,Alain Latour,José R. León
Publisher : Springer
Page : 169 pages
File Size : 52,8 Mb
Release : 2014-10-15
Category : Mathematics
ISBN : 9783319078755

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Inference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion by Corinne Berzin,Alain Latour,José R. León Pdf

This book is devoted to a number of stochastic models that display scale invariance. It primarily focuses on three issues: probabilistic properties, statistical estimation and simulation of the processes considered. It will be of interest to probability specialists, who will find here an uncomplicated presentation of statistics tools and to those statisticians who wants to tackle the most recent theories in probability in order to develop Central Limit Theorems in this context; both groups will also benefit from the section on simulation. Algorithms are described in great detail, with a focus on procedures that is not usually found in mathematical treatises. The models studied are fractional Brownian motions and processes that derive from them through stochastic differential equations. Concerning the proofs of the limit theorems, the “Fourth Moment Theorem” is systematically used, as it produces rapid and helpful proofs that can serve as models for the future. Readers will also find elegant and new proofs for almost sure convergence. The use of diffusion models driven by fractional noise has been popular for more than two decades now. This popularity is due both to the mathematics itself and to its fields of application. With regard to the latter, fractional models are useful for modeling real-life events such as value assets in financial markets, chaos in quantum physics, river flows through time, irregular images, weather events and contaminant diffusio n problems.

Author : Oksana Banna,Yuliya Mishura,Kostiantyn Ralchenko,Sergiy Shklyar
Publisher : John Wiley & Sons
Page : 293 pages
File Size : 49,5 Mb
Release : 2019-04-09
Category : Mathematics
ISBN : 9781119610342

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Fractional Brownian Motion by Oksana Banna,Yuliya Mishura,Kostiantyn Ralchenko,Sergiy Shklyar Pdf

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.

Author : Vasily E. Tarasov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 327 pages
File Size : 50,7 Mb
Release : 2019-02-19
Category : Mathematics
ISBN : 9783110571721

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Applications in Physics by Vasily E. Tarasov Pdf

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fifth volume collects authoritative chapters covering several applications of fractional calculus in physics, including electrodynamics, statistical physics and physical kinetics, and quantum theory.

Author : Yuliya Mishura,Georgiy Shevchenko
Publisher : John Wiley & Sons
Page : 400 pages
File Size : 51,8 Mb
Release : 2018-01-04
Category : Mathematics
ISBN : 9781786300508

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Theory and Statistical Applications of Stochastic Processes by Yuliya Mishura,Georgiy Shevchenko Pdf

This book is concerned with the theory of stochastic processes and the theoretical aspects of statistics for stochastic processes. It combines classic topics such as construction of stochastic processes, associated filtrations, processes with independent increments, Gaussian processes, martingales, Markov properties, continuity and related properties of trajectories with contemporary subjects: integration with respect to Gaussian processes, Itȏ integration, stochastic analysis, stochastic differential equations, fractional Brownian motion and parameter estimation in diffusion models.

Author : Ralf Metzler,Carlos Mejía-Monasterio,Jürgen Vollmer
Publisher : Frontiers Media SA
Page : 221 pages
File Size : 48,9 Mb
Release : 2021-01-08
Category : Science
ISBN : 9782889663651

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Anomalous Transport: Applications, Mathematical Perspectives, and Big Data by Ralf Metzler,Carlos Mejía-Monasterio,Jürgen Vollmer Pdf

Author : Mehmet Yavuz,Necati Özdemir
Publisher : Bentham Science Publishers
Page : 275 pages
File Size : 40,7 Mb
Release : 2022-12-14
Category : Mathematics
ISBN : 9789815051940

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Fractional Calculus: New Applications in Understanding Nonlinear Phenomena by Mehmet Yavuz,Necati Özdemir Pdf

In the last two decades, many new fractional operators have appeared, often defined using integrals with special functions in the kernel as well as their extended or multivariable forms. Modern operators in fractional calculus have different properties which are comparable to those of classical operators.These have been intensively studied formodelling and analysing real-world phenomena. There is now a growing body of research on new methods to understand natural occurrences and tackle different problems. This book presents ten reviews of recent fractional operators split over three sections: 1. Chaotic Systems and Control (covers the Caputo fractional derivative, and a chaotic fractional-order financial system)2. Heat Conduction (covers the Duhamel theorem for time-dependent source terms, and the Cattaneo–Hristov model for oscillatory heat transfer)3. Computational Methods and Their Illustrative Applications (covers mathematical analysis for understanding 5 real-word phenomena: HTLV-1 infection of CD4+ T-cells, traveling waves, rumor-spreading, biochemical reactions, and the computational fluid dynamics of a non-powered floating object navigating in an approach channel) This volume is a resource for researchers in physics, biology, behavioral sciences, and mathematics who are interested in new applications of fractional calculus in the study of nonlinear phenomena.

Author : Vladimir Panov
Publisher : Springer
Page : 511 pages
File Size : 40,7 Mb
Release : 2017-11-21
Category : Mathematics
ISBN : 9783319653136

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Modern Problems of Stochastic Analysis and Statistics by Vladimir Panov Pdf

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.

Author : H.T. Banks,K. Kunisch
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461237006

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Estimation Techniques for Distributed Parameter Systems by H.T. Banks,K. Kunisch Pdf

The research detailed in this monograph was originally motivated by our interest in control problems involving partial and delay differential equations. Our attempts to apply control theory techniques to such prob lems in several areas of science convinced us that in the need for better and more detailed models of distributed/ continuum processes in biology and mechanics lay a rich, interesting, and challenging class of fundamen tal questions. These questions, which involve science and mathematics, are typical of those arising in inverse or parameter estimation problems. Our efforts on inverse problems for distributed parameter systems, which are infinite dimensional in the most common realizations, began about seven years ago at a time when rapid advances in computing capabilities and availability held promise for significant progress in the development of a practically useful as well as theoretically sound methodology for such problems. Much of the research reported in our presentation was not begun when we outlined the plans for this monograph some years ago. By publishing this monograph now, when only a part of the originally intended topics are covered (see Chapter VII in this respect), we hope to stimulate the research and interest of others in an area of scientific en deavor which has exceeded even our optimistic expectations with respect to excitement, opportunity, and stimulation. The computer revolution alluded to above and the development of new codes allow one to solve rather routinely certain estimation problems that would have been out of the question ten years ago.

Author : Krzysztof J. Latawiec,Marian Łukaniszyn,Rafał Stanisławski
Publisher : Springer
Page : 295 pages
File Size : 53,6 Mb
Release : 2014-08-16
Category : Technology & Engineering
ISBN : 9783319099002

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Advances in Modelling and Control of Non-integer-Order Systems by Krzysztof J. Latawiec,Marian Łukaniszyn,Rafał Stanisławski Pdf

This volume presents selected aspects of non-integer, or fractional order systems, whose analysis, synthesis and applications have increasingly become a real challenge for various research communities, ranging from science to engineering. The spectrum of applications of the fractional order calculus has incredibly expanded, in fact it would be hard to find a science/engineering-related subject area where the fractional calculus had not been incorporated. The content of the fractional calculus is ranged from pure mathematics to engineering implementations and so is the content of this volume. The volume is subdivided into six parts, reflecting particular aspects of the fractional order calculus. The first part contains a single invited paper on a new formulation of fractional-order descriptor observers for fractional-order descriptor continous LTI systems. The second part provides new elements to the mathematical theory of fractional-order systems. In the third part of this volume, a bunch of new results in approximation, modeling and simulations of fractional-order systems is given. The fourth part presents new solutions to some problems in controllability and control of non-integer order systems, in particular fractional PID-like control. The fifth part analyzes the stability of non-integer order systems and some new results are offered in this important respect, in particular for discrete-time systems. The final, sixth part of this volume presents a spectrum of applications of the noninteger order calculus, ranging from bi-fractional filtering, in particular of electromyographic signals, through the thermal diffusion and advection diffusion processes to the SIEMENS platform implementation. This volume's papers were all subjected to stimulating comments and discussions from the active audience of the RRNR'2014, the 6th Conference on Non-integer Order Calculus and Its Applications that was organized by the Department of Electrical, Control and Computer Engineering, Opole University of Technology, Opole, Poland.