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