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February, 1973 Non-Anticipative Representations of Equivalent Gaussian Processes
G. Kallianpur, H. Oodaira
Ann. Probab. 1(1): 104-122 (February, 1973). DOI: 10.1214/aop/1176997027


Given two equivalent Gaussian processes the notion of a non-anticipative representation of one of the processes with respect to the other is defined. The main theorem establishes the existence of such a representation under very general conditions. The result is applied to derive such representations explicitly in two important cases where one of the processes is (i) a Wiener process, and (ii) a $N$-ple Gaussian Markov process. Radon-Nikodym derivatives are also discussed.


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G. Kallianpur. H. Oodaira. "Non-Anticipative Representations of Equivalent Gaussian Processes." Ann. Probab. 1 (1) 104 - 122, February, 1973.


Published: February, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0293.60030
MathSciNet: MR420822
Digital Object Identifier: 10.1214/aop/1176997027

Keywords: Equivalent Gaussian processes , factorization , representation , Volterra operators

Rights: Copyright © 1973 Institute of Mathematical Statistics

Vol.1 • No. 1 • February, 1973
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