 Integration of covariance kernels and stationarityRudolf Lasinger Stochastic Processes and their Applications, 1993, vol. 45, issue 2, 309-318 Abstract: The necessary and sufficient matrix condition of Mitchell, Morris and Ylvisaker (1990) for a stationary Gaussian process to have a specified process as kth derivative is investigated. The mean-square smoothing approach of stationary processes requires integration of covariance functions preserving stationarity. By providing a recursive representation of the involved reproducing kernel Hilbert spaces it is possible to analyse another criterion for k-fold integration of a process. This criterion only contains inequalities for the variances of the integrated processes. If the Hilbert space associated with the covariance function has a special form, which often occurs, then it can be shown that such processes can be integrated arbitrarily often. This is especially the case for the Ornstein-Uhlenbeck process. The results are applied to the linear and the exponential kernel and yield explicit norms in the corresponding reproducing kernel Hilbert spaces for each integration. Keywords: mean-square; integration; stationary; process; reproducing; kernel; Hilbert; space; Ornstein-Uhlenbeck; process (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:45:y:1993:i:2:p:309-318 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.