Regularity of generalized stochastic processes and their derivatives
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- by Lewis Pakula PDF
- Proc. Amer. Math. Soc. 46 (1974), 399-401 Request permission
Abstract:
If $X$ is a generalized stochastic process which is regular in the prediction-theoretic sense then $P(d/dx)X$ is regular for a differential operator $P(d/dx)$. This is used to study sufficient conditions for regularity of stationary processes. On the other hand, an example shows that the derivative of a (nonstationary) deterministic process may be regular.References
- K. Balagangadharan, The prediction theory of stationary random distributions, Mem. Coll. Sci. Univ. Kyoto Ser. A. Math. 33 (1960/61), 243–256. MR 123354, DOI 10.1215/kjm/1250775910
- Chandrakant Mahadeorao Deo, Prediction theory of non-stationary processes, Sankhyā Ser. A 27 (1965), 113–132. MR 217852
- Ju. A. Rozanov, On the extrapolation of generalized stationary random processes, Teor. Veroyatnost. i Primenen 4 (1959), 465–471 (Russian, with English summary). MR 0115216
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 46 (1974), 399-401
- MSC: Primary 60G20
- DOI: https://doi.org/10.1090/S0002-9939-1974-0350838-9
- MathSciNet review: 0350838