@Article{Alpay2013,
author = "Alpay, Daniel and Kipnis, Alon",
title = "A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes",
journal = "Opuscula Math.",
year = "2013",
volume = "33",
number = "3",
pages = "395--417",
doi = "http://dx.doi.org/10.7494/OpMath.2013.33.3.395",
url = "http://dx.doi.org/10.7494/OpMath.2013.33.3.395",
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",
issn = "1232-9274"
}