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The paper studies stochastic integration with respect to Gaussian processesand fields. It is more convenient to work with a field than a process: bydefinition, a field is a collection of stochastic integrals for a class ofdeterministic integrands. The problem is then to extend the definition torandom integrands. An orthogonal decomposition of chaos space of the randomfield leads to two such extensions, corresponding to the \Ito-Skorokhod and theStratononovich integrals, and provides an efficient tool to study theseintegrals, both analytically and numerically. For a Gaussian process, a naturaldefinition of the integral follows from a canonical correspondence betweenrandom processes and a special class of random fields.

From Random Processes to Generalized Fields: A Unified Approach to Stochastic Integration