Convergence of densities of some functionals of Gaussian processes
نویسندگان
چکیده
We study the convergence of densities of a sequence of random variables to a normal density. The random variables considered are nonlinear functionals of a Gaussian process. The tool we are using is the Malliavin calculus, in particular, the integration by parts formula and the Stein’s method. Applications to the convergence of densities of the least square estimator for the drift parameter in Ornstein-Ulenbeck is also considered. The main difficulty in application is the verification of non-degeneracy of random variables. We address this difficulty for random variables in the second Wiener chaos, and connect it to the upper bound estimate in small deviation theory.
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