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Non-central limit theorem for non-linear functionals of vector valued Gaussian stationary random fields

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  • Major, Péter

Abstract

This paper contains the multivariate generalization of the non-central limit theorems for non-linear functionals of vector valued stationary random fields under appropriate conditions proved in paper [7]. Previously A. M. Arcones presented such a result in Theorem 6 of his paper [1]. But there are some gaps in his proof which will be explained in the main text. To get this explanation the theory of the Gaussian stationary random fields described in the work [13] had to be generalized to the case of vector valued random fields. This was done in the work consisting of two subsequent papers [14] and [15]. The present paper provides a proof of the limit theorems with the help of their results.

Suggested Citation

  • Major, Péter, 2026. "Non-central limit theorem for non-linear functionals of vector valued Gaussian stationary random fields," Stochastic Processes and their Applications, Elsevier, vol. 200(C).
    • Handle: RePEc:eee:spapps:v:200:y:2026:i:c:s0304414926001377
    DOI: 10.1016/j.spa.2026.105005
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