Diffusion processes and stochastic calculus / Fabrice Baudoin

This is a concise, elegant and well-executed introduction to stochastic calculus. The text is based on a graduate level lecture course given by the author. As a consequence it is fairly self-contained and written with a style that is easy to digest. What sets this book apart from other texts on stochastic calculus is the final two chapters, where the author gives simple introductions to two modern (and lively) fields of stochastic analysis—Malliavin calculus and rough path theory. These two chapters showcase the author's talent in providing a simple account of complicated theories. Another highlight is the treatment of Dirichlet forms and diffusion semigroups, which is less commonly found in introductory texts.
The text contains hundreds of exercises which help reinforce ideas introduced in proofs and point out potential applications. Each chapter is capped off with a brief literature review, which can be extremely useful to graduate students seeking a broader picture. ... (MathSciNet)

Bibliogr. p. [269]-273. Notes bibliogr. Index