Convergence of Densities of Some Functionals of Gaussian Processes

Fei Lu, University of Kansas
May 2nd, 2012 at 4PM–5PM in 939 Evans Hall [Map]

We characterize the convergence of densities to the standard normal density for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Parallel results for the multidimensional case and for general random variables are also studied. Applications to sequences of random variables on the second Wiener chaos are introduced, in particular the convergence of densities of the Ornstein–Ulenbeck parameter estimator.