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

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  • Ileana Iribarren
  • José R. León

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.

Suggested Citation

  • Ileana Iribarren & José R. León, 2006. "Central limit theorem for solutions of random initialized differential equations: a simple proof," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-20, March.
    • Handle: RePEc:hin:jnijsa:035206
    DOI: 10.1155/JAMSA/2006/35206
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