Mathematical Modelling: Theory and Applications

Modeling with Itô Stochastic Differential Equations

Authors: Allen, E.

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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)


Table of contents (1 chapters)

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4020-5953-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-1-4020-5952-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-90-481-7487-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Modeling with Itô Stochastic Differential Equations
Authors
Series Title
Mathematical Modelling: Theory and Applications
Series Volume
22
Copyright
2007
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-1-4020-5953-7
DOI
10.1007/978-1-4020-5953-7
Hardcover ISBN
978-1-4020-5952-0
Softcover ISBN
978-90-481-7487-4
Series ISSN
1386-2960
Edition Number
1
Number of Pages
XII, 230
Topics