Malliavin calculus, geometric mixing, and expansion of diffusion functionals (Q1578966)

The aim of this work is to obtain asymptotic expansions (as time tends to infinity) for functionals of some processes; the framework covers both time series (such as ARMA processes) and diffusions with jumps. The main tool is Malliavin's calculus, and the results hold true under a nondegeneracy condition of the Malliavin covariance. As an example, the authors consider a continuous diffusion \(X_t\) satisfying a strong Hörmander condition and another condition implying the existence of a unique invariant probability measure; then if \(Z_t\) is a semimartingale which is the stochastic integral of a function of \(X_t\), they obtain an asymptotic expansion for the law of \(Z_t/\sqrt t\).