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-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.
D. Alpay and A. Kipnis. A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes. Opuscula Mathematica, vol. 33 (2013), pp. 395-417.
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This article was originally published in Opuscula Mathematica, volume 33, issue 3, in 2013 DOI: 10.7494/OpMath.2013.33.3.395