Stochastic Differential Equations For Science And Engineering

Author : Uffe Høgsbro Thygesen
Publisher : CRC Press
Page : 381 pages
File Size : 40,5 Mb
Release : 2023-06-15
Category : Mathematics
ISBN : 9781000884999

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Stochastic Differential Equations for Science and Engineering by Uffe Høgsbro Thygesen Pdf

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

Author : K. Sobczyk
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 40,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9789401137126

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Stochastic Differential Equations by K. Sobczyk Pdf

'Et moi, ..~ si lavait su CO.llUlJalt en revc:nir, One acMcc matbcmatica bu JaIdcred the human rac:c. It bu put COIDIDOD _ beet je n'y serais point aBe.' Jules Verne wbac it bdoup, 0Jl!be~ IbcII _t to!be dusty cauialcr Iabc & d 'diMardod__ The series is divergent; thc:reforc we may be -'. I!.ticT. Bc:I1 able to do something with it. O. Hcavisidc Mathematics is a tool for thought. A highly necessary tool in a world when: both feedback and non linearities abound. Similarly. all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statcmalts as: 'One service topology has rendered mathematical physics ...-; 'One service logic has rendered c0m puter science ... '; 'One service category theory has rendered mathematics ... '. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series. This series, Mathematics and Its Applications. started in 19n. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope. At the time I wrote "Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However. the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branc:hes. It also happens, quite often in fact, that branches which were thought to be completely

Author : Douglas Henderson,Peter Plaschko
Publisher : World Scientific
Page : 240 pages
File Size : 47,6 Mb
Release : 2006-08-01
Category : Science
ISBN : 9789814480536

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Stochastic Differential Equations In Science And Engineering (With Cd-rom) by Douglas Henderson,Peter Plaschko Pdf

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.

Author : Mircea Grigoriu
Publisher : Springer Science & Business Media
Page : 784 pages
File Size : 51,5 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9780817682286

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Stochastic Calculus by Mircea Grigoriu Pdf

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.

Author : Rong SITU
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 48,9 Mb
Release : 2006-05-06
Category : Technology & Engineering
ISBN : 9780387251752

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Theory of Stochastic Differential Equations with Jumps and Applications by Rong SITU Pdf

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.

Author : K. Sobczyk
Publisher : Springer
Page : 400 pages
File Size : 51,9 Mb
Release : 2011-12-24
Category : Mathematics
ISBN : 9401137137

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Stochastic Differential Equations by K. Sobczyk Pdf

Author : Soong
Publisher : Academic Press
Page : 326 pages
File Size : 52,6 Mb
Release : 1973-09-21
Category : Computers
ISBN : 9780080956121

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Random Differential Equations in Science and Engineering by Soong Pdf

Random Differential Equations in Science and Engineering

Author : Vincenzo Capasso,David Bakstein
Publisher : Springer Nature
Page : 560 pages
File Size : 49,5 Mb
Release : 2021-06-18
Category : Mathematics
ISBN : 9783030696535

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An Introduction to Continuous-Time Stochastic Processes by Vincenzo Capasso,David Bakstein Pdf

This textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across different fields. Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the Itô Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic differential equations. An Introduction to Continuous-Time Stochastic Processes, Fourth Edition is intended for graduate students taking an introductory course on stochastic processes, applied probability, stochastic calculus, mathematical finance, or mathematical biology. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. Researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering will also find this volume to be of interest, particularly the applications explored in the second half of the book.

Author : Tobias Neckel,Florian Rupp
Publisher : Walter de Gruyter
Page : 650 pages
File Size : 48,9 Mb
Release : 2013-12-17
Category : Mathematics
ISBN : 9788376560267

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Random Differential Equations in Scientific Computing by Tobias Neckel,Florian Rupp Pdf

This book is a holistic and self-contained treatment of the analysis and numerics of random differential equations from a problem-centred point of view. An interdisciplinary approach is applied by considering state-of-the-art concepts of both dynamical systems and scientific computing. The red line pervading this book is the two-fold reduction of a random partial differential equation disturbed by some external force as present in many important applications in science and engineering. First, the random partial differential equation is reduced to a set of random ordinary differential equations in the spirit of the method of lines. These are then further reduced to a family of (deterministic) ordinary differential equations. The monograph will be of benefit, not only to mathematicians, but can also be used for interdisciplinary courses in informatics and engineering.

Author : Bernt Oksendal
Publisher : Springer Science & Business Media
Page : 199 pages
File Size : 42,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662025741

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Stochastic Differential Equations by Bernt Oksendal Pdf

From the reviews: "The author, a lucid mind with a fine pedagogical instinct, has written a splendid text. He starts out by stating six problems in the introduction in which stochastic differential equations play an essential role in the solution. Then, while developing stochastic calculus, he frequently returns to these problems and variants thereof and to many other problems to show how the theory works and to motivate the next step in the theoretical development. Needless to say, he restricts himself to stochastic integration with respect to Brownian motion. He is not hesitant to give some basic results without proof in order to leave room for "some more basic applications... The book can be an ideal text for a graduate course, but it is also recommended to analysts (in particular, those working in differential equations and deterministic dynamical systems and control) who wish to learn quickly what stochastic differential equations are all about." Acta Scientiarum Mathematicarum, Tom 50, 3-4, 1986#1 "The book is well written, gives a lot of nice applications of stochastic differential equation theory, and presents theory and applications of stochastic differential equations in a way which makes the book useful for mathematical seminars at a low level. (...) The book (will) really motivate scientists from non-mathematical fields to try to understand the usefulness of stochastic differential equations in their fields." Metrica#2

Author : Frank Beichelt
Publisher : CRC Press
Page : 438 pages
File Size : 53,6 Mb
Release : 2006-02-22
Category : Mathematics
ISBN : 142001045X

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Stochastic Processes in Science, Engineering and Finance by Frank Beichelt Pdf

This book presents a self-contained introduction to stochastic processes with emphasis on their applications in science, engineering, finance, computer science, and operations research. It provides theoretical foundations for modeling time-dependent random phenomena in these areas and illustrates their application by analyzing numerous practical examples. The treatment assumes few prerequisites, requiring only the standard mathematical maturity acquired by undergraduate applied science students. It includes an introductory chapter that summarizes the basic probability theory needed as background. Numerous exercises reinforce the concepts and techniques discussed and allow readers to assess their grasp of the subject. Solutions to most of the exercises are provided in an appendix. While focused primarily on practical aspects, the presentation includes some important proofs along with more challenging examples and exercises for those more theoretically inclined. Mastering the contents of this book prepares readers to apply stochastic modeling in their own fields and enables them to work more creatively with software designed for dealing with the data analysis aspects of stochastic processes.

Author : T.T. Soong
Publisher : Unknown
Page : 327 pages
File Size : 41,9 Mb
Release : 1973
Category : Electronic
ISBN : OCLC:906330680

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Random Differential Equations in Science and Engineeing by T.T. Soong Pdf

Author : Bernt Karsten Øksendal
Publisher : Springer Science & Business Media
Page : 186 pages
File Size : 53,6 Mb
Release : 1989
Category : Distribution (Probability theory)
ISBN : 3540517405

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Stochastic Differential Equations by Bernt Karsten Øksendal Pdf

From the reviews: "The author, a lucid mind with a fine pedagogical instinct, has written a splendid text. He starts out by stating six problems in the introduction in which stochastic differential equations play an essential role in the solution. Then, while developing stochastic calculus, he frequently returns to these problems and variants thereof and to many other problems to show how the theory works and to motivate the next step in the theoretical development. Needless to say, he restricts himself to stochastic integration with respect to Brownian motion. He is not hesitant to give some basic results without proof in order to leave room for "some more basic applications... The book can be an ideal text for a graduate course, but it is also recommended to analysts (in particular, those working in differential equations and deterministic dynamical systems and control) who wish to learn quickly what stochastic differential equations are all about." Acta Scientiarum Mathematicarum, Tom 50, 3-4, 1986#1 "The book is well written, gives a lot of nice applications of stochastic differential equation theory, and presents theory and applications of stochastic differential equations in a way which makes the book useful for mathematical seminars at a low level. (...) The book (will) really motivate scientists from non-mathematical fields to try to understand the usefulness of stochastic differential equations in their fields." Metrica#2

Author : Peter E. Kloeden,Eckhard Platen
Publisher : Springer Science & Business Media
Page : 666 pages
File Size : 46,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662126165

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Numerical Solution of Stochastic Differential Equations by Peter E. Kloeden,Eckhard Platen Pdf

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP

Author : Kazimierz Sobczyk
Publisher : Unknown
Page : 400 pages
File Size : 55,8 Mb
Release : 1991
Category : Stochastic differential equations
ISBN : OCLC:23956213

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Stochastic Differential Equations by Kazimierz Sobczyk Pdf