Stochastic Differential Equations For Science And Engineering
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Stochastic Differential Equations In Science And Engineering With Cd Rom
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Author : Douglas Henderson
language : en
Publisher: World Scientific
Release Date : 2006-08-01
Stochastic Differential Equations In Science And Engineering With Cd Rom written by Douglas Henderson and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-01 with Science categories.
Traditionally, non-quantum physics has been concerned with deterministic equations where the dynamics of the system are completely determined by initial conditions. A century ago the discovery of Brownian motion showed that nature need not be deterministic. However, it is only recently that there has been broad interest in nondeterministic and even chaotic systems, not only in physics but in ecology and economics. On a short term basis, the stock market is nondeterministic and often chaotic. Despite its significance, there are few books available that introduce the reader to modern ideas in stochastic systems. This book provides an introduction to this increasingly important field and includes a number of interesting applications.
Stochastic Differential Equations For Science And Engineering
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Author : Uffe Høgsbro Thygesen
language : en
Publisher:
Release Date : 2023
Stochastic Differential Equations For Science And Engineering written by Uffe Høgsbro Thygesen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Stochastic differential equations categories.
"Stochastic Differential Equations for Science and Engineering is aimed at students at the M.Sc. and PhD level. The book describes the mathematical construction of stochastic differential equations with a level of detail suitable to the audience, while also discussing applications to estimation, stability analysis, and control. The book includes numerous examples and challenging exercises. Computational aspects are central to the approach taken in the book, so the text is accompanied by a repository on GitHub containing a toolbox in R which implements algorithms described in the book, code that regenerates all figures, and solutions to exercises. Features Contains numerous exercises, examples, and applications Suitable for science and engineering students at Master's or PhD level Thorough treatment of the mathematical theory combined with an accessible treatment of motivating examples GitHub repository available at: https://github.com/Uffe-H-Thygesen/SDEbook and https://github.com/Uffe-H-Thygesen/SDEtools"--
Stochastic Calculus
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Author : Mircea Grigoriu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Stochastic Calculus written by Mircea Grigoriu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
Algebraic, differential, and integral equations are used in the applied sciences, en gineering, economics, and the social sciences to characterize the current state of a physical, economic, or social system and forecast its evolution in time. Generally, the coefficients of and/or the input to these equations are not precisely known be cause of insufficient information, limited understanding of some underlying phe nomena, and inherent randonmess. For example, the orientation of the atomic lattice in the grains of a polycrystal varies randomly from grain to grain, the spa tial distribution of a phase of a composite material is not known precisely for a particular specimen, bone properties needed to develop reliable artificial joints vary significantly with individual and age, forces acting on a plane from takeoff to landing depend in a complex manner on the environmental conditions and flight pattern, and stock prices and their evolution in time depend on a large number of factors that cannot be described by deterministic models. Problems that can be defined by algebraic, differential, and integral equations with random coefficients and/or input are referred to as stochastic problems. The main objective of this book is the solution of stochastic problems, that is, the determination of the probability law, moments, and/or other probabilistic properties of the state of a physical, economic, or social system. It is assumed that the operators and inputs defining a stochastic problem are specified.
Applied Stochastic Differential Equations
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Author : Simo Särkkä
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-02
Applied Stochastic Differential Equations written by Simo Särkkä and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-02 with Business & Economics categories.
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
An Introduction To The Numerical Simulation Of Stochastic Di Erential Equations
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Author : Desmond J. Higham
language : en
Publisher: SIAM
Release Date : 2021-01-28
An Introduction To The Numerical Simulation Of Stochastic Di Erential Equations written by Desmond J. Higham and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-28 with Mathematics categories.
This book provides a lively and accessible introduction to the numerical solution of stochastic differential equations with the aim of making this subject available to the widest possible readership. It presents an outline of the underlying convergence and stability theory while avoiding technical details. Key ideas are illustrated with numerous computational examples and computer code is listed at the end of each chapter. The authors include 150 exercises, with solutions available online, and 40 programming tasks. Although introductory, the book covers a range of modern research topics, including Itô versus Stratonovich calculus, implicit methods, stability theory, nonconvergence on nonlinear problems, multilevel Monte Carlo, approximation of double stochastic integrals, and tau leaping for chemical and biochemical reaction networks. An Introduction to the Numerical Simulation of Stochastic Differential Equations is appropriate for undergraduates and postgraduates in mathematics, engineering, physics, chemistry, finance, and related disciplines, as well as researchers in these areas. The material assumes only a competence in algebra and calculus at the level reached by a typical first-year undergraduate mathematics class, and prerequisites are kept to a minimum. Some familiarity with basic concepts from numerical analysis and probability is also desirable but not necessary.
International Encyclopedia Of Statistical Science
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Author : Miodrag Lovric
language : en
Publisher: Springer Nature
Release Date : 2025-06-19
International Encyclopedia Of Statistical Science written by Miodrag Lovric and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Mathematics categories.
The International Encyclopedia of Statistical Science stands as a monumental effort to enrich statistics education globally, particularly in regions facing educational challenges. By amalgamating the expertise of over 700 authors from 110 countries, including Nobel Laureates and presidents of statistical societies, it offers an unparalleled resource for readers worldwide. This encyclopedia is not just a collection of entries; it is a concerted effort to revive statistics as a vibrant, critical field of study and application. Providing a comprehensive and accessible account of statistical terms, methods, and applications, it enables readers to gain a quick insight into the subject, regardless of their background. This work serves to refresh and expand the knowledge of researchers, managers, and practitioners, highlighting the relevance and applicability of statistics across various fields, from economics and business to healthcare and public policy. Furthermore, it aims to inspire students by demonstrating the significance of statistics in solving real-world problems, thus encouraging a new generation to explore and contribute to the field.
Mathematics In Engineering Sciences
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Author : Mangey Ram
language : en
Publisher: CRC Press
Release Date : 2019-09-09
Mathematics In Engineering Sciences written by Mangey Ram and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-09 with Mathematics categories.
This book includes research studies, novel theory, as well as new methodology and applications in mathematics and management sciences. The book will provide a comprehensive range of mathematics applied to engineering areas for different tasks. It will offer an international perspective and a bridge between classical theory and new methodology in many areas, along with real-life applications. Features Offers solutions to multi-objective transportation problem under cost reliability using utility function Presents optimization techniques to support eco-efficiency assessment in manufacturing processes Covers distance-based function approach for optimal design of engineering processes with multiple quality characteristics Provides discrete time sliding mode control for non-linear networked control systems Discusses second law of thermodynamics as instruments for optimizing fluid dynamic systems and aerodynamic systems
Computational Mathematics And Applications
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Author : Dia Zeidan
language : en
Publisher: Springer Nature
Release Date : 2020-11-23
Computational Mathematics And Applications written by Dia Zeidan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-23 with Mathematics categories.
This book is a collection of invited and reviewed chapters on state-of-the-art developments in interdisciplinary mathematics. The book discusses recent developments in the fields of theoretical and applied mathematics, covering areas of interest to mathematicians, scientists, engineers, industrialists, researchers, faculty, and students. Readers will be exposed to topics chosen from a wide range of areas including differential equations, integral reforms, operational calculus, numerical analysis, fluid mechanics, and computer science. The aim of the book is to provide brief and reliably expressed research topics that will enable those new or not aware of mathematical sciences in this part of the world. While the book has not been precisely planned to address any branch of mathematics, it presents contributions of the relevant topics to do so. The topics chosen for the book are those that we have found of significant interest to many researchers in the world. These also are topics that are applicable in many fields of computational and applied mathematics. This book constitutes the first attempt in Jordanian literature to scientifically consider the extensive need of research development at the national and international levels with which mathematics deals. The book grew not only from the international collaboration between the authors but rather from the long need for a research-based book from different parts of the world for researchers and professionals working in computational and applied mathematics. This is the modified version of the back-cover content on the print book
Using R For Numerical Analysis In Science And Engineering
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Author : Victor A. Bloomfield
language : en
Publisher: CRC Press
Release Date : 2018-09-03
Using R For Numerical Analysis In Science And Engineering written by Victor A. Bloomfield and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Mathematics categories.
Instead of presenting the standard theoretical treatments that underlie the various numerical methods used by scientists and engineers, Using R for Numerical Analysis in Science and Engineering shows how to use R and its add-on packages to obtain numerical solutions to the complex mathematical problems commonly faced by scientists and engineers. This practical guide to the capabilities of R demonstrates Monte Carlo, stochastic, deterministic, and other numerical methods through an abundance of worked examples and code, covering the solution of systems of linear algebraic equations and nonlinear equations as well as ordinary differential equations and partial differential equations. It not only shows how to use R’s powerful graphic tools to construct the types of plots most useful in scientific and engineering work, but also: Explains how to statistically analyze and fit data to linear and nonlinear models Explores numerical differentiation, integration, and optimization Describes how to find eigenvalues and eigenfunctions Discusses interpolation and curve fitting Considers the analysis of time series Using R for Numerical Analysis in Science and Engineering provides a solid introduction to the most useful numerical methods for scientific and engineering data analysis using R.
Taylor Approximations For Stochastic Partial Differential Equations
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Author : Arnulf Jentzen
language : en
Publisher: SIAM
Release Date : 2011-12-08
Taylor Approximations For Stochastic Partial Differential Equations written by Arnulf Jentzen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-08 with Mathematics categories.
This book presents a systematic theory of Taylor expansions of evolutionary-type stochastic partial differential equations (SPDEs). The authors show how Taylor expansions can be used to derive higher order numerical methods for SPDEs, with a focus on pathwise and strong convergence. In the case of multiplicative noise, the driving noise process is assumed to be a cylindrical Wiener process, while in the case of additive noise the SPDE is assumed to be driven by an arbitrary stochastic process with H?lder continuous sample paths. Recent developments on numerical methods for random and stochastic ordinary differential equations are also included since these are relevant for solving spatially discretised SPDEs as well as of interest in their own right. The authors include the proof of an existence and uniqueness theorem under general assumptions on the coefficients as well as regularity estimates in an appendix.