Modeling with Ito Stochastic Differential Equations

By: E. Allen

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eText | 8 March 2007

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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 It?? 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.