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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Zero-one laws for Gaussian processes


Author: G. Kallianpur
Journal: Trans. Amer. Math. Soc. 149 (1970), 199-211
MSC: Primary 60.50
DOI: https://doi.org/10.1090/S0002-9947-1970-0266293-4
MathSciNet review: 0266293
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Abstract: Some zero-one laws are proved for Gaussian processes defined on linear spaces of functions. They are generalizations of a result for Wiener measure due to R. H. Cameron and R. E. Graves. The proofs exploit an interesting relationship between a Gaussian process and its reproducing kernel Hilbert space. Applications are discussed.


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DOI: https://doi.org/10.1090/S0002-9947-1970-0266293-4
Keywords: Gaussian processes, zero-one laws, reproducing kernel Hilbert space
Article copyright: © Copyright 1970 American Mathematical Society