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.
@article{1176997027,
author = {Kallianpur, G. and Oodaira, H.},
title = {Non-Anticipative Representations of Equivalent Gaussian Processes},
journal = {Ann. Probab.},
volume = {1},
number = {5},
year = {1973},
pages = { 104-122},
language = {en},
url = {http://dml.mathdoc.fr/item/1176997027}
}
Kallianpur, G.; Oodaira, H. Non-Anticipative Representations of Equivalent Gaussian Processes. Ann. Probab., Tome 1 (1973) no. 5, pp. 104-122. http://gdmltest.u-ga.fr/item/1176997027/