Abstract: In previous works, we have developed a new Malliavin calculus on the Poisson space based on the lent particle formula. The aim of this work is to prove that, on the Wiener space for the standard Ornstein-Uhlenbeck structure, we also have such a formula which permits to calculate easily and intuitively the Malliavin derivative of a functional. Our approach uses chaos extensions associa...

The derivative of the log-likelihood function, known as score function, plays a central role in parametric statistical inference. It can be used to study the asymptotic behavior of likelihood and pseudo-likelihood estimators. For instance, one can deduce the local asymptotic normality property which leads to various asymptotic properties of these estimators. In this article we apply Malliavin C...

By using Malliavin calculus for Lévy processes, we compute an explicit martingale representation for the maximum of a square-integrable Lévy process.

We show how to use the Malliavin calculus to obtain a new exact formula for the density ρ of the law of any random variable Z which is measurable and di erentiable with respect to a given isonormal Gaussian process. The main advantage of this formula is that it does not refer to the divergence operator (dual of the Malliavin derivative). In particular, density lower bounds can be obtained in so...

This monograph contains some recent results by the authors and their collaborators on the application of Stein’s method combined with Malliavin calculus to the normal approximation for functionals of a Gaussian process. It is addressed to researchers and graduate students in probability and statistics who would like to learn the basis of Gaussian analysis and its application to asymptotic techn...

We give a new characterization for the convergence in distribution to a standard normal law of a sequence of multiple stochastic integrals of a fixed order with variance one, in terms of the Malliavin derivatives of the sequence. We also give a new proof of the main theorem in [7] using techniques of Malliavin calculus. Finally, we extend our result to the multidimensional case and prove a weak...

In this paper we provide a Monte Carlo algorithm for the density estimation of functionals of spatial point processes on Lipschitz domains with random marks, using the Malliavin calculus. Our method allows us to compute explicitly the Malliavin weight and is applied to density estimation of the interference in a wireless ad hoc network model. This extends and makes more precise some recent resu...

We give a new characterization for the convergence in distribution to a standard normal law of a sequence of multiple stochastic integrals of a fixed order with variance one, in terms of the Malliavin derivatives of the sequence. We also give a new proof of the main theorem in [7] using techniques of Malliavin calculus. Finally, we extend our result to the multidimensional case and prove a weak...