This volume gives a unified presentation of stochastic analysis for continuous and discontinuous stochastic processes, in both discrete and continuous time. It is mostly self-contained and accessible to graduate students and researchers having already received a basic training in probability. The simultaneous treatment of continuous and jump processes is done in the framework of normal martingales; that includes the Brownian motion and compensated Poisson processes as specific cases. In particular, the basic tools of stochastic analysis (chaos representation, gradient, divergence, integration by parts) are presented in this general setting. Applications are given to functional and deviation inequalities and mathematical finance.

From the reviews:

"The author presents several aspects of stochastic analysis for discrete and continuous-time normal martingales. ? variety of operators on the Poisson space is an highlight of this book. ? It is finally worth mentioning that this volume of the Lecture Notes in Mathematics includes many interesting applications and that the various notions, properties and proofs are clear and detailed." (A. Réveillac, Zentralblatt MATH, Vol. 1185, 2010)

"The book under review has the original feature of giving a unified treatment to all normal martingales. ? The book is quite accessible to beginners. ? its main goal is providing advanced researchers with a study of stochastic analysis in both discrete and continuous time and with a simultaneous treatment of both continuous and jump processes." (Dominique Lépingle, Mathematical Reviews, Issue 2011 j)