Stochastic Calculus

by Richard Durrett

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.

Genres: Mathematics

352 pages, Hardcover

First published January 1, 1996

About the author

Richard Timothy Durrett is a mathematician known for his research and books on mathematical probability theory, stochastic processes and their application to mathematical ecology and population genetics.

He received his BS and MS at Emory University in 1972 and 1973 and his Ph.D. at Stanford University in 1976 under advisor Donald Iglehart. From 1985 until 2010 was on the faculty at Cornell University. Since 2010, Durrett has been a professor at Duke University.

He was elected to the United States National Academy of Sciences in 2007. In 2012 he became a fellow of the American Mathematical Society.[1]

Durrett is the founder of the Cornell Probability Summer Schools, and he is still its scientific organizer.