Overview
- A procedure is thoroughly explained for constructing realistic stochastic differential equation models
- Many stochastic differential equation models are developed for randomly varying systems in biology, physics, and finance
- Random variables, stochastic processes, stochastic integration, and stochastic differential equations are explained in a Hilbert space setting which unifies and simplifies the presentation
- The text is useful for researchers and graduate students with many interesting exercises and computer programs provided throughout the text
Part of the book series: Mathematical Modelling: Theory and Applications (MMTA, volume 22)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Dynamical systems with random influences occur throughout the physical, biological, and social sciences. By carefully studying a randomly varying system over a small time interval, a discrete stochastic process model can be constructed. Next, letting the time interval shrink to zero, an Ito stochastic differential equation model for the dynamical system is obtained.
This modeling procedure is thoroughly explained and illustrated for randomly varying systems in population biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation. Computer programs, given throughout the text, are useful in solving representative stochastic problems. Analytical and computational exercises are provided in each chapter that complement the material in the text.
Modeling with Itô Stochastic Differential Equations is useful for researchers and graduate students. As a textbook for a graduate course, prerequisites include probability theory, differential equations, intermediate analysis, and some knowledge of scientific programming.
Reviews
From the reviews:
"The author of this book has carefully selected and well described basic notions and concepts from probability theory and stochastic processes … . His goal is … to address the book to a wide category of readers, applied scientists, who need to use these sophisticated tools in their work. … Besides researchers … this book is suitable as a text for graduate university courses. I enjoyed reading the book and my expectation is that it will be met with interest by the readers." (Jordan M. Stoyanov, Zentralblatt MATH, Vol. 1130, 2008)
"This text sets out to provide a reasonably concise and accessible account of the extensive range of concepts and procedures that are used in producing and handling SDEMs, and by and large it succeeds. … On the whole, the selection of material is very good; the author has succeeded in producing an account of the subject that is manageably compact and yet reasonably wide-ranging in its illustrative applications. … the book can indeed be firmly recommended." (David Stirzaker, SIAM Review, Vol. 50 (2), 2008)
Authors and Affiliations
Bibliographic Information
Book Title: Modeling with Itô Stochastic Differential Equations
Authors: E. Allen
Series Title: Mathematical Modelling: Theory and Applications
DOI: https://doi.org/10.1007/978-1-4020-5953-7
Publisher: Springer Dordrecht
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media B.V. 2007
Hardcover ISBN: 978-1-4020-5952-0Published: 09 March 2007
Softcover ISBN: 978-90-481-7487-4Published: 16 November 2010
eBook ISBN: 978-1-4020-5953-7Published: 08 March 2007
Series ISSN: 1386-2960
Edition Number: 1
Number of Pages: XII, 230
Topics: Probability Theory and Stochastic Processes, Applications of Mathematics, Analysis, Mathematical Modeling and Industrial Mathematics, Computational Mathematics and Numerical Analysis