A GENERALIZED WHITE NOISE SPACE APPROACH TO STOCHASTIC INTEGRATION FOR A CLASS OF GAUSSIAN STATIONARY INCREMENT PROCESSES

Given a Gaussian stationary increment processes, we show that a Skorokhod-Hitsuda stochastic integral with respect to this process, which obeys the Wick-Ito calculus rules, can be naturally defined using ideas taken from Hida's white noise space theory. We use the Bochner-Minlos theorem to associate a probability space to the process, and define the counterpart of the S-transform in this space. We then use this transform to define the stochastic integral and prove an associated Ito formula.