It is shown that for a suitable definition of the nonadapted Stratonovich stochastic integral, the existence of the Ogawa integral implies that the Stratonovich integral exists and the two are equal.
@article{1176991172,
author = {Nualart, D. and Zakai, M.},
title = {On the Relation Between the Stratonovich and Ogawa Integrals},
journal = {Ann. Probab.},
volume = {17},
number = {4},
year = {1989},
pages = { 1536-1540},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991172}
}
Nualart, D.; Zakai, M. On the Relation Between the Stratonovich and Ogawa Integrals. Ann. Probab., Tome 17 (1989) no. 4, pp. 1536-1540. http://gdmltest.u-ga.fr/item/1176991172/