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This book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents th

Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics

While the original works on Malliavin calculus aimed to study the smoothness of densities of solutions to stochastic differential equations, this book has anoth

A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.

The stochastic calculus of variations of Paul Malliavin (1925 - 2010), known today as the Malliavin Calculus, has found many applications, within and beyond the