Approximation of Sojourn Times of Gaussian Processes

作者：Debicki, Krzysztof; Michna, Zbigniew; Peng, Xiaofan^*

来源：Methodology and Computing in Applied Probability, 2019, 21(4): 1183-1213.

DOI：10.1007/s11009-018-9667-7

• Sojourn time
• Occupation time
• Exact asymptotics
• Gaussian process
• Locally stationary processes

We investigate the tail asymptotic behavior of the sojourn time for a large class of centered Gaussian processes X, in both continuous- and discrete-time framework. All results obtained here are new for the discrete-time case. In the continuous-time case, we complement the investigations of Berman (Commun Pure Appl Math 38(5):519-528, 1985a and Probab Theory Relat Fields 20(1):113-124, 1987) for non-stationary X. A by-product of our investigation is a new representation of Pickands constant which is important for Monte-Carlo simulations and yields a sharp lower bound for Pickands constant.

• 出版日期2019-12
• 单位电子科技大学