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Proceedings of the American Mathematical Society

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Regularity of generalized stochastic processes and their derivatives

Author: Lewis Pakula
Journal: Proc. Amer. Math. Soc. 46 (1974), 399-401
MSC: Primary 60G20
MathSciNet review: 0350838
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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.

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  • [1] K. Balagangadharan, The prediction theory of stationary random distributions, Mem. Coll. Sci. Univ. Kyoto Ser. A Math. 33 (1960/61), 243-256. MR 23 #A682. MR 0123354 (23:A682)
  • [2] C. M. Deo, Prediction theory of non-stationary processes, Sankyhā Ser. A 27 (1965), 113-132. MR 36 #941. MR 0217852 (36:941)
  • [3] Ju. Rozanov, On the extrapolation of generalized stationary random processes, Teor. Verojatnost. i Primenen. 4 (1959), 465-471 = Theor. Probability Appl. 4 (1959), 426-431. MR 22 #6018. MR 0115216 (22:6018)

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Keywords: Prediction theory of generalized stochastic processes
Article copyright: © Copyright 1974 American Mathematical Society

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