We give a simple representation of two-parameter martingales in terms of a stochastic integral. This representation leads to the idea of the partial derivate of a martingale and to a generalization of the stochastic Green's theorem of the authors. Green's formula in this generalized form gives us a new and simpler proof of the fact that the derivative of a holomorphic process is holomorphic.
"Martingale Representations and Holomorphic Processes." Ann. Probab. 5 (4) 511 - 521, August, 1977. https://doi.org/10.1214/aop/1176995757