http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
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. 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. This time-saving 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.
1. Brownian Motion -- 2. Stochastic Integration -- 3. Brownian Motion, II -- 4. Partial Differential Equations -- 5. Stochastic Differential Equations -- 6. One Dimensional Diffusions -- 7. Diffusions as Markov Processes -- 8. Weak Convergence.
Includes bibliographical references and index.
Brownian motion and martingales in analysis