Baricz, A. (2026) Journal of Mathematical Analysis and Applications [Matematică, Q2]

Publicat: 01 Septembrie 2025

Baricz, A. (2026) The Hermite rank of a special subordinated long-memory Gaussian process. Journal of Mathematical Analysis and Applications, 554(1), 129910.

DOI: https://doi.org/10.1016/j.jmaa.2025.129910

✓ Publisher: Elsevier
✓ Categories: Mathematics; Mathematics, Applied
✓ Article Influence Score (AIS): 0.632 (2024) / Q2

Abstract: Recently, Y. Feng et al. [2] introduced two long-memory subordinated Gaussian processes and they studied non-central and central limit theorems for the sample variance of these processes under different conditions and based on modified Bessel functions of the second kind. In order to investigate the Hermite rank for the sinh-arcsinh normal process, they studied the first and second Hermite coefficients of a specific transformation. In this paper our aim is to show the corresponding positivity (and absolute monotonicity) results of the first two Hermite coefficients of a special Hermite expansion, which involves the modified Bessel function of the second kind. Our results on modified Bessel functions of the second kind show that the Hermite rank in question is 1 or 2, depending on the value of the skewness parameter.

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