Author	Stroock, Daniel W. author
Title	Multidimensional Diffusion Processes [electronic resource] / by Daniel W. Stroock, S. R. Srinivasa Varadhan
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997
Connect to	http://dx.doi.org/10.1007/3-540-28999-2
Descript	XII, 338 p. online resource

From the reviews: "โฆ Both the Markov-process approach and the Itรด approach โฆ have been immensely successful in diffusion theory. The Stroock-Varadhan book, developed from the historic 1969 papers by its authors, presents the martingale-problem approach as a more powerful - and, in certain regards, more intrinsic-means of studying the foundations of the subject. [โฆ] โฆ the authors make the uncompromising decision not "to proselytise by intimidating the reader with myriad examples demonstrating the full scope of the techniques", but rather to persuade the reader "with a careful treatment of just one problem to which they apply". [โฆ] Most of the main tools of stochastic-processes theory are used, ..but it is the formidable combination of probability theory with analysis โฆ which is the core of the work. [โฆ] I have emphasized the great importance of the Stroock-Varadhan book. It contains a lot more than I have indicated; in particular, its many exercises conain much interesting material. For immediate confirmation of the subject's sparkle, virtuosity, and depth, see โฆ McKean ('s 1969 book). The Stroock-Varadhan book proceeds on its inexorable way like a massive Bach fugue. โฆ But old J.S. can e something of knockout if his themes get hold of you. And his influence on what followed was 8you may say) substantial." David Williams in the Bulletin of the American Mathematical Society

Preliminary Material: Extension Theorems, Martingales, and Compactness -- Markov Processes, Regularity of Their Sample Paths, and the Wiener Measure -- Parabolic Partial Differential Equations -- The Stochastic Calculus of Diffusion Theory -- Stochastic Differential Equations -- The Martingale Formulation -- Uniqueness -- Itรด's Uniqueness and Uniqueness to the Martingale Problem -- Some Estimates on the Transition Probability Functions -- Explosion -- Limit Theorems -- The Non-unique Case

1. Mathematics
2. Probabilities
3. Physics
4. Mathematics
5. Probability Theory and Stochastic Processes
6. Theoretical
7. Mathematical and Computational Physics