# Malliavin calculus¶

My list of publications which are related to Malliavin calculus per se

## The latest publications¶

### Malliavin calculus for independent random variables¶

Abstract: On any denumerable product of probability spaces, we construct a Malliavin gradient and then a divergence and a number operator. This yields a Dirichlet structure which can be shown to approach the usual structures for Poisson and Brownian processes. We obtain versions of almost all the classical functional inequalities in discrete settings which show that the Efron-Stein inequality can be interpreted as a Poincaré inequality or that Hoeffding decomposition of U-statistics can be interpreted as a chaos decomposition. We obtain a version of the Lyapounov central limit theorem for independent random variables without resorting to ad-hoc couplings, thus increasing the scope of the Stein method.

To appear in Stochastic processes and their applications

@article{decreusefond:hal-01565240,
TITLE = {{Malliavin and Dirichlet structures for independent random variables}},
AUTHOR = {Decreusefond, Laurent and Halconruy, H{'e}l{e}ne},
URL = {https://hal.archives-ouvertes.fr/hal-01565240},
JOURNAL = {{Stochastic Processes and their Applications}},
PUBLISHER = {{Elsevier}},
YEAR = {2018},
KEYWORDS = {Talagrand inequality ; Talagrand   inequality ; Stein method ; Malliavin calculus ; Lyapounov CLT ; log-Sobolev inequality ; Dirichlet structure ; Ewens distribution},
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