... way of interpreting the Malliavin derivative of a given random vari-able F = F(ω), ω ∈ Ω, on the given probability space (Ω, F,P) is to regardit as a derivative with respect to the random parameter ... difference operator.How to use this bookIt is the purpose of this book to give an introductory presentation of the theory of Malliavin calculus and its applications, mainly to finance. For pedagogicalreasons, ... derivative (or stochastic gradient)ofF at t.This gives a simple and intuitive interpretation of the Malliavin deriva-tive in the Brownian motion case. Moreover, some of the basic properties of calculus...