Stochastic Analysis of Mixed Fractional Gaussian Processes PDF Download
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Author: Yuliya Mishura
Publisher: Elsevier
ISBN: 0081023634
Category : Mathematics
Languages : en
Pages : 212
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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
Author: Yuliya Mishura
Publisher: Elsevier
ISBN: 0081023634
Category : Mathematics
Languages : en
Pages : 212
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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
Author: Vladimir Panov
Publisher: Springer
ISBN: 331965313X
Category : Mathematics
Languages : en
Pages : 506
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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.
Author: Anatoliy Malyarenko
Publisher: Springer Nature
ISBN: 3031178203
Category : Mathematics
Languages : en
Pages : 907
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Book Description
The goal of the 2019 conference on Stochastic Processes and Algebraic Structures held in SPAS2019, Västerås, Sweden, from September 30th to October 2nd 2019, was to showcase the frontiers of research in several important areas of mathematics, mathematical statistics, and its applications. The conference was organized around the following topics 1. Stochastic processes and modern statistical methods,2. Engineering mathematics,3. Algebraic structures and their applications. The conference brought together a select group of scientists, researchers, and practitioners from the industry who are actively contributing to the theory and applications of stochastic, and algebraic structures, methods, and models. The conference provided early stage researchers with the opportunity to learn from leaders in the field, to present their research, as well as to establish valuable research contacts in order to initiate collaborations in Sweden and abroad. New methods for pricing sophisticated financial derivatives, limit theorems for stochastic processes, advanced methods for statistical analysis of financial data, and modern computational methods in various areas of applied science can be found in this book. The principal reason for the growing interest in these questions comes from the fact that we are living in an extremely rapidly changing and challenging environment. This requires the quick introduction of new methods, coming from different areas of applied science. Advanced concepts in the book are illustrated in simple form with the help of tables and figures. Most of the papers are self-contained, and thus ideally suitable for self-study. Solutions to sophisticated problems located at the intersection of various theoretical and applied areas of the natural sciences are presented in these proceedings.
Author: Oksana Banna
Publisher: John Wiley & Sons
ISBN: 1119610346
Category : Mathematics
Languages : en
Pages : 294
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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.
Author:
Publisher: Elsevier
ISBN: 0443293295
Category : Mathematics
Languages : en
Pages : 828
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Book Description
Probability Models, Volume 51 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on Stein's methods, Probabilities and thermodynamics third law, Random Matrix Theory, General tools for understanding fluctuations of random variables, An approximation scheme to compute the Fisher-Rao distance between multivariate normal distributions, Probability Models Applied to Reliability and Availability Engineering, Backward stochastic differential equation– Stochastic optimization theory and viscous solution of HJB equation, and much more.Additional chapters cover Probability Models in Machine Learning, The recursive stochastic algorithm, randomized urn models and response-adaptive randomization in clinical trials, Random matrix theory: local laws and applications, KOO methods and their high-dimensional consistencies in some multivariate models, Fourteen Lectures on Inference for Stochastic Processes, and A multivariate cumulative damage model and some applications. - Provides the latest information on probability models - Offers outstanding and original reviews on a range of probability models research topics - Serves as an indispensable reference for researchers and students alike
Author: Yuliya Mishura
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110654245
Category : Mathematics
Languages : en
Pages : 390
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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.
Author: Yeliz Karaca
Publisher: Academic Press
ISBN: 0323886167
Category : Science
Languages : en
Pages : 352
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Book Description
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, mathematics-informed and data driven processes aside from the means of modelling, and simulations for the solution of multifaceted problems characterized by nonlinearity, non-regularity and self-similarity, frequently encountered in different complex systems. The fundamental interacting components underlying complexity, complexity thinking, processes and theory along with computational processes and technologies, with machine learning as the core component of AI demonstrate the enabling of complex data to augment some critical human skills. Appealing to an interdisciplinary network of scientists and researchers to disseminate the theory and application in medicine, neurology, mathematics, physics, biology, chemistry, information theory, engineering, computer science, social sciences and other far-reaching domains, the overarching aim is to empower out-of-the-box thinking through multifarious methods, directed towards paradoxical situations, uncertain processes, chaotic, transient and nonlinear dynamics of complex systems. - Constructs and presents a multifarious approach for critical decision-making processes embodying paradoxes and uncertainty. - Includes a combination of theory and applications with regard to multi-chaos, fractal and multi-fractional as well as AI of different complex systems and many-body systems. - Provides readers with a bridge between application of advanced computational mathematical methods and AI based on comprehensive analyses and broad theories.
Author: Christopher C. Bernido
Publisher: Birkhäuser
ISBN: 3319072455
Category : Mathematics
Languages : en
Pages : 304
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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.
Author: Yuliya Mishura
Publisher: Springer Science & Business Media
ISBN: 3540758720
Category : Mathematics
Languages : en
Pages : 411
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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.
Author: Kęstutis Kubilius
Publisher: Springer
ISBN: 3319710303
Category : Mathematics
Languages : en
Pages : 403
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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.
