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Density convergence in the Breuer-Major theorem for Gaussian stationary sequences
Hu, Yaozhong Nualart, David Tindel, Samy Xu, Fangjun
Hu, Yaozhong
Nualart, David
Tindel, Samy
Xu, Fangjun
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Abstract
Consider a Gaussian stationary sequence with unit variance X={Xk;k∈N∪{0}}. Assume that the central limit theorem holds for a weighted sum of the form Vn=n−1/2∑n−1k=0f(Xk), where f designates a finite sum of Hermite polynomials. Then we prove that the uniform convergence of the density of Vn towards the standard Gaussian density also holds true, under a mild additional assumption involving the causal representation of X.
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2015
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Bernoulli Society for Mathematical Statistics and Probability
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Nualart_2015.pdf
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Hu, Y., Nualart, D., Tindel, S., & Xu, F. (2015). Density convergence in the Breuer–Major theorem for Gaussian stationary sequences. Bernoulli, 21(4), 2336-2350.