Modeling with Itô Stochastic Differential Equations

ISBN-13: 9781402059520 / Angielski / Twarda / 2007 / 230 str.

Edward Allen; E. Allen

Opis

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 Ito 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."

Recenzje

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)

Spis treści

Random Variables.- Stochastic Processes.- Stochastic Integration.- Stochastic Differential Equations.- Modeling.

O autorze

Edward Allen has taught for more than thirty years as a faculty member at the Massachusetts Institute of Technology and Yale University, and as an invited guest at institutions in the U.S., South America, Europe, and Asia. He is a Fellow of the American Institute of Architects. He has designed more than fifty constructed buildings and is the bestselling author of The Architect's Studio Companion, Architectural Detailing, Fundamentals of Residential Construction, and Shaping Structures: Statics, all published by Wiley.