Central limit theorem for solutions of random initialized differential equations: a simple proof

Iribarren, Ileana; León, José R.

doi:https://doi.org/10.1155/JAMSA/2006/35206

International Journal of Stochastic Analysis

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Volume 2006 | Article ID 035206 | https://doi.org/10.1155/JAMSA/2006/35206

Central limit theorem for solutions of random initialized differential equations: a simple proof

Ileana Iribarren¹and José R. León¹

Received13 Nov 2004

Revised12 May 2005

Accepted13 May 2005

Published27 Mar 2006

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.

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Copyright

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.

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