Analytic Nonstationary Processes
In 1952, Cramér introduced a class of nonstationary processes. This broad class of processes contains the important harmonizable and stationary classes of processes. The Cramér class can have additional structure imposed upon it through Cesáro summability considerations. This paper obtains conditions for the analyticity of the sample paths of a class of these processes. A sampling theorem is presented as a natural application.
AMS Subject Classification60G12 60G35
KeywordsHarmonizable processes: Cramér processes analytic processes
Unable to display preview. Download preview PDF.
- Besicovitch, A.S., 1954. Almost Periodic Functions. Dover Publications, Inc., New York.Google Scholar
- Chang, D. K., Rao, M.M., 1986. Bimeasures and Nonstationary Processes. Real and Stochastic Analysis. pages 7–118, John Wiley and Sons, New York.Google Scholar
- Cramér, H., 1952. A Contribution to the Theory of Stochastic Processes. Proc. Second Berkeley Symp Math. Statist. Prob. 2, 55–77.Google Scholar
- Rao, M.M., 1978. Covariance Analysis of Non Stationary Time Series in Developments in Statistics. Vol. 1, pages 171–275.Google Scholar
- Swift, R.J., 1997. Some Aspects of Harmonizable Processes and Fields. Real and Stochastic Analysis: Recent Advances. edited by M.M. Rao, pages 303–365, CRC Press, Boca Raton.Google Scholar