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A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes

Alpay D., Kipnis A.

Opuscula Mathematica

2013

Vol. 33, no. 3

395--417

Given a Gaussian stationary increment processes, we show that a Skorokhod-Hitsuda stochastic integral with respect to this process, which obeys the Wick-Itô 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 Itô formula.