This is not a particularly easy text, even for the apparently ordinary graduate student. Thus, before running out to work your way across the equation-dense terrain of this book, you are strongly advised (by the author and by me) to take a long hard look at a truly great review of the prerequisite materials, quietly awaiting you at http://www.siam.org/books/dc13.

The book progressively relates numerous aspects of Markov processes in continuous time. For those of you who may never patiently work through these technical topics, nor even rise to the challenge of the prerequisites, the author magnificently opens with a momentary flash of Zen enlightenment (apparently recursively inspired by Markov continuity), writing, “To five generations of women in my life.”

From that modest tribute, the author begins trekking in the rugged foothills of Poisson-Weiner processes and the calculus and MATLAB thereof, and then climbs further upward to and through the awesome glaciers of Kolmogorov equations, Feynman-Kac, Black-Scholes, Radyn-Nikodym, Levy, and Girsanov.

Now, it is clear that any neophyte to works of these titans would have benefited from an interweaving of vignettes from relevant case studies (the types that the author must inevitably recite at social functions, when in the absence of fellow colleagues from this computationally intense discipline), but there are no such items in this book. Rather, if this is material that you are already intimately familiar with, and you would like to borrow a wonderful outline of fine lecture notes, then you have come to the right book.

Graduate students too, after they have completed the course, may find this book of outstanding merit as a concise catalog of useful theorems and proofs. However, unaccompanied intellectual tourists (whom the author calls “applied mathematicians, applied probabilists, engineers, statisticians, and other scientists ... reluctant to invest time to learn it (i.e. stochastic calculus and optimal stochastic control in continuous time) from more advanced treatments relying heavily on abstract concepts”) are advised to beware. If you are in this category, there are easy wrong turns awaiting you on every other page of this book; the innate topology of these compounded stochastic cul-de-sacs might better be presented under the warning, “Enter at your own risk if unaccompanied by an expert.”

On the other hand, I concede to the author that this is a unique intuitive supplement “with important applications, such as financial market modeling.”