Gaussian lower bounds for the density via Malliavin calculus
Representations as expectation and lower bounds are derived for the probability density of a Wiener functional \(F\) using a classical integration by parts formula in the Malliavin calculus. In comparison with other approaches, those bounds only require a one-sided inequality on the term \(\langle DF,-DL^{-1}F\rangle_{L^2(\mathbb{R}_+)}\), where \(DF\) and \(L\), respectively, denote the Malliavin gradient of the functional \(F\) and the Ornstein-Uhlenbeck operator. Applications are given to additive functionals of Gaussian processes and to stochastic differential equations with fractional Brownian noise.
scientific article; zbMATH DE number 7226761