Martingale Representations and Holomorphic Processes

Abstract

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.