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Author : Aliakbar Montazer Haghighi
Release : 2010
Genre : Functions of several complex variables
Kind : eBook
Book Rating : 814/5 ( reviews)
Book Synopsis Advanced Mathematics for Engineers with Applications in Stochastic Processes by : Aliakbar Montazer Haghighi
Download or read book Advanced Mathematics for Engineers with Applications in Stochastic Processes written by Aliakbar Montazer Haghighi. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Aliakbar Montazer Haghighi
Release : 2010
Genre : Functions of several complex variables
Kind : eBook
Book Rating : 806/5 ( reviews)
Book Synopsis Advanced Mathematics for Engineers with Applications in Stochastic Processes by : Aliakbar Montazer Haghighi
Download or read book Advanced Mathematics for Engineers with Applications in Stochastic Processes written by Aliakbar Montazer Haghighi. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: Topics in advanced mathematics for engineers, probability and statistics typically span three subject areas, are addressed in three separate textbooks and taught in three different courses in as many as three semesters. Due to this arrangement, students taking these courses have had to shelf some important and fundamental engineering courses until much later than is necessary. This practice has generally ignored some striking relations that exist between the seemingly separate areas of statistical concepts, such as moments and estimation of Poisson distribution parameters. On one hand, these concepts commonly appear in stochastic processes -- for instance, in measures on effectiveness in queuing models. On the other hand, they can also be viewed as applied probability in engineering disciplines -- mechanical, chemical, and electrical, as well as in engineering technology. There is obviously, an urgent need for a textbook that recognises the corresponding relationships between the various areas and a matching cohesive course that will see through to their fundamental engineering courses as early as possible. This book is designed to achieve just that. Its seven chapters, while retaining their individual integrity, flow from selected topics in advanced mathematics such as complex analysis and wavelets to probability, statistics and stochastic processes.
Author : Alexandre J. Chorin
Release : 2014-01-21
Genre : Mathematics
Kind : eBook
Book Rating : 805/5 ( reviews)
Book Synopsis Stochastic Tools in Mathematics and Science by : Alexandre J. Chorin
Download or read book Stochastic Tools in Mathematics and Science written by Alexandre J. Chorin. This book was released on 2014-01-21. Available in PDF, EPUB and Kindle. Book excerpt: "Stochastic Tools in Mathematics and Science" covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. The topics covered include conditional expectations, stochastic processes, Brownian motion and its relation to partial differential equations, Langevin equations, the Liouville and Fokker-Planck equations, as well as Markov chain Monte Carlo algorithms, renormalization, basic statistical mechanics, and generalized Langevin equations and the Mori-Zwanzig formalism. The applications include sampling algorithms, data assimilation, prediction from partial data, spectral analysis, and turbulence. The book is based on lecture notes from a class that has attracted graduate and advanced undergraduate students from mathematics and from many other science departments at the University of California, Berkeley. Each chapter is followed by exercises. The book will be useful for scientists and engineers working in a wide range of fields and applications. For this new edition the material has been thoroughly reorganized and updated, and new sections on scaling, sampling, filtering and data assimilation, based on recent research, have been added. There are additional figures and exercises. Review of earlier edition: "This is an excellent concise textbook which can be used for self-study by graduate and advanced undergraduate students and as a recommended textbook for an introductory course on probabilistic tools in science." Mathematical Reviews, 2006
Author : Alexander S. Poznyak
Release : 2009-08-13
Genre : Technology & Engineering
Kind : eBook
Book Rating : 039/5 ( reviews)
Book Synopsis Advanced Mathematical Tools for Automatic Control Engineers: Volume 2 by : Alexander S. Poznyak
Download or read book Advanced Mathematical Tools for Automatic Control Engineers: Volume 2 written by Alexander S. Poznyak. This book was released on 2009-08-13. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Mathematical Tools for Automatic Control Engineers, Volume 2: Stochastic Techniques provides comprehensive discussions on statistical tools for control engineers. The book is divided into four main parts. Part I discusses the fundamentals of probability theory, covering probability spaces, random variables, mathematical expectation, inequalities, and characteristic functions. Part II addresses discrete time processes, including the concepts of random sequences, martingales, and limit theorems. Part III covers continuous time stochastic processes, namely Markov processes, stochastic integrals, and stochastic differential equations. Part IV presents applications of stochastic techniques for dynamic models and filtering, prediction, and smoothing problems. It also discusses the stochastic approximation method and the robust stochastic maximum principle. - Provides comprehensive theory of matrices, real, complex and functional analysis - Provides practical examples of modern optimization methods that can be effectively used in variety of real-world applications - Contains worked proofs of all theorems and propositions presented
Author : Mu-fa Chen
Release : 2021-05-25
Genre : Mathematics
Kind : eBook
Book Rating : 322/5 ( reviews)
Book Synopsis Introduction To Stochastic Processes by : Mu-fa Chen
Download or read book Introduction To Stochastic Processes written by Mu-fa Chen. This book was released on 2021-05-25. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this book is to introduce the elements of stochastic processes in a rather concise manner where we present the two most important parts — Markov chains and stochastic analysis. The readers are led directly to the core of the main topics to be treated in the context. Further details and additional materials are left to a section containing abundant exercises for further reading and studying.In the part on Markov chains, the focus is on the ergodicity. By using the minimal nonnegative solution method, we deal with the recurrence and various types of ergodicity. This is done step by step, from finite state spaces to denumerable state spaces, and from discrete time to continuous time. The methods of proofs adopt modern techniques, such as coupling and duality methods. Some very new results are included, such as the estimate of the spectral gap. The structure and proofs in the first part are rather different from other existing textbooks on Markov chains.In the part on stochastic analysis, we cover the martingale theory and Brownian motions, the stochastic integral and stochastic differential equations with emphasis on one dimension, and the multidimensional stochastic integral and stochastic equation based on semimartingales. We introduce three important topics here: the Feynman-Kac formula, random time transform and Girsanov transform. As an essential application of the probability theory in classical mathematics, we also deal with the famous Brunn-Minkowski inequality in convex geometry.This book also features modern probability theory that is used in different fields, such as MCMC, or even deterministic areas: convex geometry and number theory. It provides a new and direct routine for students going through the classical Markov chains to the modern stochastic analysis.
