Opuscula Mathematica
Opuscula Math. 33, no. 3 (), 395-417
http://dx.doi.org/10.7494/OpMath.2013.33.3.395
Opuscula Mathematica

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.
Cite this article as:
Daniel Alpay, Alon Kipnis, A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes, Opuscula Math. 33, no. 3 (2013), 395-417, http://dx.doi.org/10.7494/OpMath.2013.33.3.395
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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