Density formula and concentration inequalities with Malliavin calculus
نویسندگان
چکیده
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 some instances. Among several examples, we provide an application to the (centered) maximum of a general Gaussian process, thus extending a formula recently used by Chatterjee [4]. We also explain how to derive concentration inequalities for Z in our framework.
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