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.
"On the Relation Between the Stratonovich and Ogawa Integrals." Ann. Probab. 17 (4) 1536 - 1540, October, 1989. https://doi.org/10.1214/aop/1176991172