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Journal of Applied Mathematics and Stochastic Analysis - Volume 2006 2006, Article ID 35206, 20 pages

Escuela de Matemática, Facultad de Ciencias, Universidad Central de Venezuela, A.P. 47197 Los Chaguaramos, Caracas 1041-A, Venezuela

Received 13 November 2004; Revised 12 May 2005; Accepted 13 May 2005

Copyright © 2006 Ileana Iribarren and José R. León. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the central and noncentral limit theorems for theconvolution of a certain kernel h with Fξ⋅, 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 theinitial Gaussian process by an m-dependent process. We could saythat only variance computations are needed to get the two types oflimits. Then we apply the obtained results to the solutions of thecertain differential equations.





Autor: Ileana Iribarren and José R. León

Fuente: https://www.hindawi.com/



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