On the limit properties of the last exit time and the first crossing point for the stationary dependent chi-sequences

Abstract

In this paper, we studied the limit properties of the last exit time and the first crossing point for the stationary dependent chi-sequences which are generated by stationary weakly and strongly dependent Gaussian sequences. It is shown that the last exit time and the first crossing point are asymptotically independent and dependent for weakly and strongly dependent case, respectively.

Keywords:

• The last exit time
• the first crossing point
• stationary Gaussian sequences
• chi-sequences

AMS CLASSIFICATION:

• Primary 62F15
• secondary 60G70

Acknowledgments

The authors would like to thank the referee and the editor for the thorough reading and valuable suggestions.

Additional information

Funding

Research was supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. LY18A010020), Xinmiao Talents Project of Zhejiang Province of China (Grant No. 2020R417018) and SRT of Jiaxing University.