Download or read book Stochastic Analysis of Mixed Fractional Gaussian Processes written by Yuliya Mishura and published by Elsevier. This book was released on 2018-05-26 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Stochastic Calculus for Fractional Brownian Motion and Related Processes written by Yuliya Mishura and published by Springer Science & Business Media. This book was released on 2008-01-02 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stochastic Analysis for Gaussian Random Processes and Fields written by Vidyadhar S. Mandrekar and published by CRC Press. This book was released on 2015-06-23 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Analysis for Gaussian Random Processes and Fields: With Applications presents Hilbert space methods to study deep analytic properties connecting probabilistic notions. In particular, it studies Gaussian random fields using reproducing kernel Hilbert spaces (RKHSs).The book begins with preliminary results on covariance and associated RKHS
Download or read book Stochastic Analysis written by Jean-Pierre Fouque and published by . This book was released on 1996 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Processes Statistical Methods and Engineering Mathematics written by Anatoliy Malyarenko and published by Springer Nature. This book was released on 2023-01-26 with total page 907 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fractional Brownian Motion written by Oksana Banna and published by John Wiley & Sons. This book was released on 2019-04-09 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modern Problems of Stochastic Analysis and Statistics written by Vladimir Panov and published by Springer. This book was released on 2017-11-21 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stable Non Gaussian Random Processes written by Gennady Samoradnitsky and published by Routledge. This book was released on 2017-11-22 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves as a standard reference, making this area accessible not only to researchers in probability and statistics, but also to graduate students and practitioners. The book assumes only a first-year graduate course in probability. Each chapter begins with a brief overview and concludes with a wide range of exercises at varying levels of difficulty. The authors supply detailed hints for the more challenging problems, and cover many advances made in recent years.
Download or read book Discrete Time Approximations and Limit Theorems written by Yuliya Mishura and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-10-25 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Non Gaussian Selfsimilar Stochastic Processes written by Ciprian Tudor and published by Springer Nature. This book was released on 2023-07-04 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the field of stochastic analysis of Hermite processes. These selfsimilar stochastic processes with stationary increments live in a Wiener chaos and include the fractional Brownian motion, the only Gaussian process in this class. Using the Wiener chaos theory and multiple stochastic integrals, the book covers the main properties of Hermite processes and their multiparameter counterparts, the Hermite sheets. It delves into the probability distribution of these stochastic processes and their sample paths, while also presenting the basics of stochastic integration theory with respect to Hermite processes and sheets. The book goes beyond theory and provides a thorough analysis of physical models driven by Hermite noise, including the Hermite Ornstein-Uhlenbeck process and the solution to the stochastic heat equation driven by such a random perturbation. Moreover, it explores up-to-date topics central to current research in statistical inference for Hermite-driven models.
Download or read book Stochastic Partial Differential Equations With Additive Gaussian Noise Analysis And Inference written by Ciprian A Tudor and published by World Scientific. This book was released on 2022-10-11 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stochastic partial differential equations (SPDEs) arise in many applications of the probability theory. This monograph will focus on two particular (and probably the most known) equations: the stochastic heat equation and the stochastic wave equation.The focus is on the relationship between the solutions to the SPDEs and the fractional Brownian motion (and related processes). An important point of the analysis is the study of the asymptotic behavior of the p-variations of the solutions to the heat or wave equations driven by space-time Gaussian noise or by a Gaussian noise with a non-trivial correlation in space.The book is addressed to public with a reasonable background in probability theory. The idea is to keep it self-contained and avoid using of complex techniques. We also chose to insist on the basic properties of the random noise and to detail the construction of the Wiener integration with respect to them. The intention is to present the proofs complete and detailed.
Download or read book Multi Chaos Fractal and Multi Fractional Artificial Intelligence of Different Complex Systems written by Yeliz Karaca and published by Academic Press. This book was released on 2022-06-22 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Analysis of Variations for Self similar Processes written by Ciprian A. Tudor and published by Springer. This book was released on 2013-09-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Gaussian Processes written by Takeyuki Hida and published by American Mathematical Soc.. This book was released on with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at students and researchers in mathematics, communications engineering, and economics, this book describes the probabilistic structure of a Gaussian process in terms of its canonical representation (or its innovation process). Multiple Markov properties of a Gaussian process and equivalence problems of Gaussian processes are clearly presented. The authors' approach is unique, involving causality in time evolution and information-theoretic aspects. Because the book is self-contained and only requires background in the fundamentals of probability theory and measure theory, it would be suitable as a textbook at the senior undergraduate or graduate level.
Download or read book Seminar on Stochastic Analysis Random Fields and Applications IV written by Robert Dalang and published by Birkhäuser. This book was released on 2012-12-06 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains twenty refereed papers presented at the 4th Seminar on Stochastic Processes, Random Fields and Applications, which took place in Ascona, Switzerland, from May 2002. The seminar focused mainly on stochastic partial differential equations, stochastic models in mathematical physics, and financial engineering. The book will be a valuable resource for researchers in stochastic analysis and professionals interested in stochastic methods in finance and insurance.
Download or read book Stochastic Processes and Applications written by Sergei Silvestrov and published by Springer. This book was released on 2018-12-05 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Parameter Estimation in Fractional Diffusion Models written by Kęstutis Kubilius and published by Springer. This book was released on 2018-01-04 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
