Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 35206, 20 pages
doi:10.1155/JAMSA/2006/35206
Abstract
We study the central and noncentral limit theorems for the
convolution of a certain kernel h with F(ξ(⋅)), where ξ is a stationary Gaussian process and F is a square integrable function with respect to the standard Gaussian measure.
Our method consists in showing that in the weak dependence case,
we can use the Lindeberg method, approaching the
initial Gaussian process by an m-dependent process. We could say
that only variance computations are needed to get the two types of
limits. Then we apply the obtained results to the solutions of the
certain differential equations.