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This book treats stochastic calculus and differential equations in some generality, while nevertheless keeping the treatment relatively elementary and accessible. By using the Bichteler-Dellacherie theorem as the basis for an approach, a rapid introduction to the subject is given. Many of the usual theorems, such as Stricker's theorem, or that a semimartingale remains a semimartingale under a change to an equivalent probability measure, are transparently simple in this context.

The second edition has several significant changes, most prominently the addition of exercises for solution. Chapter 3 has been redone, with a new and more intuitive proof of the Doob-Meyer decomposition theorem, the more general version of Girsanov's theorem due to Lenglart, the Kazamaki-Novikov criteria for expoenetial local martingales to be martingales, and a modern treatment of compensators. Chapter 4 now treats sigma martingales and gives a more comprehensive treatment of martingale representation, including the Jacod-Yor theorem. A new chapter, Chapter 6, is an introduction to the theory of the expansion of filtrations.

A new "corrected third printing"' was released in April 2005. This is essentially a new version of the second edition, with more exercises, mistakes corrected, references updated, etc.; hence it is named Version 2.1.

Solutions to selected exercises for Chapters 1,2, and 3 are now available. The solutions have been graciously provided by Kazuhiro Shimbo. Solutions.pdf

This book is intended to serve as the basis for a streamlined one semester course on measure theory based Probability Theory. It assumes no prior knowledge, and it is written with an applied audience in mind, such as Statisticians, Economists, or Engineers. Yet it is mathematically rigorous. It is designed so that one could use it for self study as well.

Solutions to selected exercises are now available. The solutions have been graciously provided by Deniz Sezer.

This book is the French version of Probability Essentials, Second Edition.

This text is a revision of the original text of Charles Morrey, Jr. and Murray Protter, Calculus and Analytic Geometry, Third Edition. It is modernized, while retaining the easy to read and yet thorough and correct style of the original.