Two related extensions of the stochastic integral are discussed. These extensions allow the integrand to anticipate the Brownian motion, and arise in the study of linear stochastic integral equations. The development is based on the homogeneous chaos expansion of the integrand. Some properties of these extended integrals, and their commutativity with the classical integrals, are derived.
"An Extension of the Stochastic Integral." Ann. Probab. 10 (2) 435 - 450, May, 1982. https://doi.org/10.1214/aop/1176993868