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

[摘要] We study the central and noncentral limit theorems for theconvolutionof a certain kernelhwithF(ξ(⋅)), whereξis a stationary Gaussian process andFis a square integrable function with respect to the standard Gaussian measure.Our method consists in showing that in the weak dependence case,we can usethe Lindeberg method, approaching theinitial Gaussian process by anm-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.

[学科分类] 应用数学