Abstract
It is shown that in the case of stationary Gaussian processes, the $J$th $(J \geq 1)$ record times $\{T_n, n \geq 1\}$ and the corresponding $J$-upper order statistics $\{X_{T_n - J + 1, T_n}, \ldots, X_{T_n, T_n}\}$ can almost surely be identified via a translation of the time index $n$ to the corresponding elements defined on a sequence of independent and identically distributed random variables. A construction method for approximating sequences of record times and the corresponding upper order statistics introduced by Haiman (1987a, b) for the case $J = 1$ is extended and applied under weaker conditions concerning the covariance function, and also under different sets of new hypotheses.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
