Stochastic Calculus

This compact yet thorough text zeros in on the parts of the theory that are useful for applications to mathematical finance, queuing theory, biology, and physics. The book 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 by treating semigroups and generators, applying the theory of Harris chains to diffusions, and presenting a quick course in weak convergence of Markov chains to diffusions.