Multidimensional Diffusion Processes

"...Both the Markov-process approach and the Itô approach ...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. [... ] ...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". [...] Most of the main tools of stochastic-processes theory are used,... but it is the formidable combination of probability theory with analysis ...which is the tore of the work. [... ] 1 have emphasized the great importance of the Stroock-Varadhan book. It contains a lot more than I have indicated; in particular, its many exercises contain much interesting material. For immediate confirmation of the subject's sparkle, virtuosity, and depth, see ...McKean's (1969 book). The Strock-Varadhan book proceeds on its inexorable way like a massive Bach fugue. ...But old J.S. tan be something of a knockout if his themes get hold of you. And his influence on what followed was (you may say) substantial!" David Williams in the Bulletin of the American Mathematical Society 1980