Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus (Cambridge Mathematical Library)

Rating:
Summary: Pretty accessible
Review: The parts of this book I've read have been clear and accessible for someone with an undergraduate degree in mathematics and some knowledge of stochastic processes. It doesn't needlessly multiply the jargon like some books, and it focuses mainly on the one-dimensional case so that the intuition isn't constantly obscured by matrix notation. Many subjects also have chatty introductions that offer intuition and a bit of relief from the hard work involved in learning this subject.

Rating:
Summary: Pretty accessible
Review: The parts of this book I've read have been clear and accessible for someone with an undergraduate degree in mathematics and some knowledge of stochastic processes. It doesn't needlessly multiply the jargon like some books, and it focuses mainly on the one-dimensional case so that the intuition isn't constantly obscured by matrix notation. Many subjects also have chatty introductions that offer intuition and a bit of relief from the hard work involved in learning this subject.

Rating:
Summary: A Great Book
Review: This book and its companion volume are a well organized and relatively easy-to-read introduction to a wide variety of ideas in stochastic processes. It is not only a great reference (I always keep it on my desk) but it also has a solid expositional style that fully motivates concepts as they are introduced. The Ito Calculus volume goes deeper than a number of other books on topic including information on integration wrt to a general semimartingale instead of just BM and even an introduction to stochastic calculus on manifolds. My only complaints about the book are that it is separated into two volumes which can be kind of a pain and that its coverage of the SDE/PDE relationship is weak. I would recommend reading Karatzas&Shreeve in addition to this book to fill in some the SDE/PDE details and to get another point of view on the somewhat difficult topic of stochastic analysis