The asymptotic relation between the first crossing point and the last exit time of Gaussian order statistics sequences

Zhijun Ning; Zhongquan Tan

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arXiv · 2303.01088

The asymptotic relation between the first crossing point and the last exit time of Gaussian order statistics sequences

Zhijun Ning·Zhongquan Tan

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Abstract

In this paper, we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences. It is shown that the first crossing point and the last exit time are asymptotically independent and dependent for weakly and strongly dependent respectively. The asymptotic relation between the first exit time and the last exit time for stationary weakly and strongly dependent Gaussian Gaussian sequences are also obtained.

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Zhijun Ning, Zhongquan Tan. 2023-03-02. The asymptotic relation between the first crossing point and the last exit time of Gaussian order statistics sequences. https://arxiv.org/abs/2303.01088

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