Level Sets and Extrema of Random Processes and Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Level Sets and Extrema of Random Processes and Fields write by Jean-Marc Azais. This book was released on 2009-02-17. Level Sets and Extrema of Random Processes and Fields available in PDF, EPUB and Kindle. A timely and comprehensive treatment of random field theory with applications across diverse areas of study Level Sets and Extrema of Random Processes and Fields discusses how to understand the properties of the level sets of paths as well as how to compute the probability distribution of its extremal values, which are two general classes of problems that arise in the study of random processes and fields and in related applications. This book provides a unified and accessible approach to these two topics and their relationship to classical theory and Gaussian processes and fields, and the most modern research findings are also discussed. The authors begin with an introduction to the basic concepts of stochastic processes, including a modern review of Gaussian fields and their classical inequalities. Subsequent chapters are devoted to Rice formulas, regularity properties, and recent results on the tails of the distribution of the maximum. Finally, applications of random fields to various areas of mathematics are provided, specifically to systems of random equations and condition numbers of random matrices. Throughout the book, applications are illustrated from various areas of study such as statistics, genomics, and oceanography while other results are relevant to econometrics, engineering, and mathematical physics. The presented material is reinforced by end-of-chapter exercises that range in varying degrees of difficulty. Most fundamental topics are addressed in the book, and an extensive, up-to-date bibliography directs readers to existing literature for further study. Level Sets and Extrema of Random Processes and Fields is an excellent book for courses on probability theory, spatial statistics, Gaussian fields, and probabilistic methods in real computation at the upper-undergraduate and graduate levels. It is also a valuable reference for professionals in mathematics and applied fields such as statistics, engineering, econometrics, mathematical physics, and biology.
Topological Complexity of Smooth Random Functions
Topological Complexity of Smooth Random Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topological Complexity of Smooth Random Functions write by Robert Adler. This book was released on 2011-05-18. Topological Complexity of Smooth Random Functions available in PDF, EPUB and Kindle. These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.
Probability and Statistical Physics in St. Petersburg
Probability and Statistical Physics in St. Petersburg - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Probability and Statistical Physics in St. Petersburg write by V. Sidoravicius. This book was released on 2016-04-28. Probability and Statistical Physics in St. Petersburg available in PDF, EPUB and Kindle. This book brings a reader to the cutting edge of several important directions of the contemporary probability theory, which in many cases are strongly motivated by problems in statistical physics. The authors of these articles are leading experts in the field and the reader will get an exceptional panorama of the field from the point of view of scientists who played, and continue to play, a pivotal role in the development of the new methods and ideas, interlinking it with geometry, complex analysis, conformal field theory, etc., making modern probability one of the most vibrant areas in mathematics.
Inference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion
Inference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Inference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion write by Corinne Berzin. This book was released on 2014-10-15. Inference on the Hurst Parameter and the Variance of Diffusions Driven by Fractional Brownian Motion available in PDF, EPUB and Kindle. 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.
Advances in Contemporary Statistics and Econometrics
Advances in Contemporary Statistics and Econometrics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in Contemporary Statistics and Econometrics write by Abdelaati Daouia. This book was released on 2021-06-14. Advances in Contemporary Statistics and Econometrics available in PDF, EPUB and Kindle. This book presents a unique collection of contributions on modern topics in statistics and econometrics, written by leading experts in the respective disciplines and their intersections. It addresses nonparametric statistics and econometrics, quantiles and expectiles, and advanced methods for complex data, including spatial and compositional data, as well as tools for empirical studies in economics and the social sciences. The book was written in honor of Christine Thomas-Agnan on the occasion of her 65th birthday. Given its scope, it will appeal to researchers and PhD students in statistics and econometrics alike who are interested in the latest developments in their field.
