SYNOPTIC ABSTRACT
The class of processes called holomorphic by Cairoli and Walsh are extended to the class of L2,2–bounded processes. In particular, the L2,2 X-holomorphic processes are shown to be Bochner L2,2–bounded and the integrals of a L2,2 X-holomorphic process are shown to preserve its L2,2 X-holomorphicity. Related to L2,2 X-holomorphic processes are certain stochastic partial derivatives. The stochastic partial derivatives are generalized to L2,2–bounded processes and the properties of path independence of the line integrals is shown to imply the existence of the derivatives. A Green's theorem is derived for stochastic partial derivatives with respect to L2,2–bounded processes.
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