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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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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DOI: https://doi.org/10.1090/S0002-9939-1974-0350838-9
Keywords: Prediction theory of generalized stochastic processes
Article copyright: © Copyright 1974 American Mathematical Society