Download or read book Stochastic Tools in Mathematics and Science written by Alexandre J Chorin and published by Springer Science & Business Media. This book was released on 2005-11-29 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to probability-based modeling covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. Topics covered include conditional expectations, stochastic processes, Langevin equations, and Markov chain Monte Carlo algorithms. The applications include data assimilation, prediction from partial data, spectral analysis and turbulence. A special feature is the systematic analysis of memory effects.
Download or read book Stochastic Tools in Mathematics and Science written by Alexandre J. Chorin and published by Springer Science & Business Media. This book was released on 2014-01-21 with total page 193 pages. 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
Download or read book Stochastic Tools in Mathematics and Science written by Alexandre Joel Chorin and published by . This book was released on 2013-05-31 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Tools in Mathematics and Science written by Alexandre Chorin and published by Springer. This book was released on 2009-08-03 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to probability-based modeling covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. Topics covered include conditional expectations, stochastic processes, Langevin equations, and Markov chain Monte Carlo algorithms. The applications include data assimilation, prediction from partial data, spectral analysis and turbulence. A special feature is the systematic analysis of memory effects.
Download or read book Stochastic Tools in Mathematics and Science written by Alexandre J Chorin and published by Springer. This book was released on 2010-11-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to probability-based modeling covers basic stochastic tools used in physics, chemistry, engineering and the life sciences. Topics covered include conditional expectations, stochastic processes, Langevin equations, and Markov chain Monte Carlo algorithms. The applications include data assimilation, prediction from partial data, spectral analysis and turbulence. A special feature is the systematic analysis of memory effects.
Download or read book Stochastic Tools in Turbulence written by John L. Lumley and published by Courier Corporation. This book was released on 2007-01-01 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible treatment offers the mathematical tools for describing and solving problems related to stochastic vector fields. Advanced undergraduates and graduate students will find its use of generalized functions a relatively simple method of resolving mathematical questions. It will prove a valuable reference for applied mathematicians and professionals in the fields of aerospace, chemical, civil, and nuclear engineering. The author, Professor Emeritus of Engineering at Cornell University, starts with a survey of probability distributions and densities and proceeds to examinations of moments, characteristic functions, and the Gaussian distribution; random functions; and random processes in more dimensions. Extensive appendixes—which include information on Fourier transforms, tensors, generalized functions, and invariant theory—contribute toward making this volume mathematically self-contained.
Download or read book Theory of Stochastic Differential Equations with Jumps and Applications written by Rong SITU and published by Springer Science & Business Media. This book was released on 2006-05-06 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.
Download or read book Stochastic Tools in Turbulence written by John L. Lumey and published by Elsevier. This book was released on 2012-12-02 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Tools in Turbulence discusses the available mathematical tools to describe stochastic vector fields to solve problems related to these fields. The book deals with the needs of turbulence in relation to stochastic vector fields, particularly, on three-dimensional aspects, linear problems, and stochastic model building. The text describes probability distributions and densities, including Lebesgue integration, conditional probabilities, conditional expectations, statistical independence, lack of correlation. The book also explains the significance of the moments, the properties of the characteristic function, and the Gaussian distribution from a more physical point of view. In considering fields, one must account for single-valued functions of one or more parameters, or collections of single-valued functions of one or more parameters such as time or space coordinates. The text also discusses multidimensional vector fields of finite energy, the characteristic eddies for a homogenous vector field, as well as, the distribution of solutions of an algebraic equation. Engineers, algebra students, and professors of statistics and advanced mathematics will find the book highly useful.
Download or read book Stochastic Simulation and Monte Carlo Methods written by Carl Graham and published by Springer Science & Business Media. This book was released on 2013-07-16 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Itô integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations.
Download or read book An Introduction to Stochastic Processes in Physics written by Don S. Lemons and published by Johns Hopkins University Press+ORM. This book was released on 2003-04-29 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This “lucid, masterfully written introduction to an often difficult subject . . . belongs on the bookshelf of every student of statistical physics” (Dr. Brian J. Albright, Applied Physics Division, Los Alamos National Laboratory). This book provides an accessible introduction to stochastic processes in physics and describes the basic mathematical tools of the trade: probability, random walks, and Wiener and Ornstein-Uhlenbeck processes. With an emphasis on applications, it includes end-of-chapter problems. Physicist and author Don S. Lemons builds on Paul Langevin’s seminal 1908 paper “On the Theory of Brownian Motion” and its explanations of classical uncertainty in natural phenomena. Following Langevin’s example, Lemons applies Newton’s second law to a “Brownian particle on which the total force included a random component.” This method builds on Newtonian dynamics and provides an accessible explanation to anyone approaching the subject for the first time. This volume contains the complete text of Paul Langevin’s “On the Theory of Brownian Motion,” translated by Anthony Gythiel.
Download or read book Recent Development in Stochastic Dynamics and Stochastic Analysis written by Jinqiao Duan and published by World Scientific. This book was released on 2010 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic dynamical systems and stochastic analysis are of great interests not only to mathematicians but also scientists in other areas. Stochastic dynamical systems tools for modeling and simulation are highly demanded in investigating complex phenomena in, for example, environmental and geophysical sciences, materials science, life sciences, physical and chemical sciences, finance and economics. The volume reflects an essentially timely and interesting subject and offers reviews on the recent and new developments in stochastic dynamics and stochastic analysis, and also some possible future research directions. Presenting a dozen chapters of survey papers and research by leading experts in the subject, the volume is written with a wide audience in mind ranging from graduate students, junior researchers to professionals of other specializations who are interested in the subject.
Download or read book Advanced Mathematical Tools for Automatic Control Engineers Volume 2 written by Alexander S. Poznyak and published by Elsevier. This book was released on 2009-08-13 with total page 568 pages. 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
Download or read book Stochastic Methods for Modeling and Predicting Complex Dynamical Systems written by Nan Chen and published by Springer Nature. This book was released on 2023-03-13 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book enables readers to understand, model, and predict complex dynamical systems using new methods with stochastic tools. The author presents a unique combination of qualitative and quantitative modeling skills, novel efficient computational methods, rigorous mathematical theory, as well as physical intuitions and thinking. An emphasis is placed on the balance between computational efficiency and modeling accuracy, providing readers with ideas to build useful models in practice. Successful modeling of complex systems requires a comprehensive use of qualitative and quantitative modeling approaches, novel efficient computational methods, physical intuitions and thinking, as well as rigorous mathematical theories. As such, mathematical tools for understanding, modeling, and predicting complex dynamical systems using various suitable stochastic tools are presented. Both theoretical and numerical approaches are included, allowing readers to choose suitable methods in different practical situations. The author provides practical examples and motivations when introducing various mathematical and stochastic tools and merges mathematics, statistics, information theory, computational science, and data science. In addition, the author discusses how to choose and apply suitable mathematical tools to several disciplines including pure and applied mathematics, physics, engineering, neural science, material science, climate and atmosphere, ocean science, and many others. Readers will not only learn detailed techniques for stochastic modeling and prediction, but will develop their intuition as well. Important topics in modeling and prediction including extreme events, high-dimensional systems, and multiscale features are discussed.
Download or read book Stochastic Programming 84 written by András Prékopa and published by North Holland. This book was released on 1986 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Models In The Life Sciences And Their Methods Of Analysis written by Wan Frederic Y M and published by World Scientific. This book was released on 2019-08-29 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biological processes are evolutionary in nature and often evolve in a noisy environment or in the presence of uncertainty. Such evolving phenomena are necessarily modeled mathematically by stochastic differential/difference equations (SDE), which have been recognized as essential for a true understanding of many biological phenomena. Yet, there is a dearth of teaching material in this area for interested students and researchers, notwithstanding the addition of some recent texts on stochastic modelling in the life sciences. The reason may well be the demanding mathematical pre-requisites needed to 'solve' SDE.A principal goal of this volume is to provide a working knowledge of SDE based on the premise that familiarity with the basic elements of a stochastic calculus for random processes is unavoidable. Through some SDE models of familiar biological phenomena, we show how stochastic methods developed for other areas of science and engineering are also useful in the life sciences. In the process, the volume introduces to biologists a collection of analytical and computational methods for research and applications in this emerging area of life science. The additions broaden the available tools for SDE models for biologists that have been limited by and large to stochastic simulations.
Download or read book Stochastic Modeling written by Barry L. Nelson and published by Courier Corporation. This book was released on 2012-10-11 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coherent introduction to techniques also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Includes formulation of models, analysis, and interpretation of results. 1995 edition.
Download or read book Physics of Stochastic Processes written by Reinhard Mahnke and published by John Wiley & Sons. This book was released on 2009-08-04 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures given by one of the authors with many years of experience in teaching stochastic processes, this textbook is unique in combining basic mathematical and physical theory with numerous simple and sophisticated examples as well as detailed calculations. In addition, applications from different fields are included so as to strengthen the background learned in the first part of the book. With its exercises at the end of each chapter (and solutions only available to lecturers) this book will benefit students and researchers at different educational levels. Solutions manual available for lecturers on www.wiley-vch.de
