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Synopsis
This compact yet thorough text zeros in on the parts of the theory that are particularly relevant to applications . It begins with a description of Brownian motion and the associated stochastic calculus, including their relationship to partial differential equations. It solves stochastic differential equations by a variety of methods and studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions, and presenting a quick course in weak convergence of Markov chains to diffusions.
The presentation is unparalleled in its clarity and simplicity. Whether your students are interested in probability, analysis, differential geometry or applications in operations research, physics, finance, or the many other areas to which the subject applies, you'll find that this text brings together the material you need to effectively and efficiently impart the practical background they need.
Booknews
An introductory text pinpointing the stochastic theories useful for application to mathematical finance, queuing, biology, and physics. Durrett (mathematics, Cornell U.) describes Brownian motion and associated stochastic calculus, the relationship to partial differential equations, solves the equations by a variety of methods, and includes treatments of semigroups, generators, Harris chains to diffusions, and weak convergence of Markov chains to diffusions. Road-tested in the classrooms of Cornell, the volume features student friendly solutions for exercises and simplifies content to its essential elements. Annotation c. Book News, Inc., Portland, OR (booknews.com)