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Dynamical systems with random influences occur throughout the physical, biological, and social sciences. A discrete stochastic process model can be constructed by carefully studying a randomly varying system over a small time interval. Next, an Ito stochastic differential equation model for the dynamical system can be obtained by letting the time interval shrink to zero. This book thoroughly explains and illustrates this modeling procedure 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. Each chapter provides analytical and computational exercises that complement the material in the text.
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