Opuscula Math. 33, no. 3 (2013), 395-417
A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes
Abstract. 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.
Keywords: stochastic integral, white noise space, fractional Brownian motion.
Mathematics Subject Classification: 60H40, 60H05.