Stochastic integration for a wide class of Gaussian stationary increment processes using an extension of the S-transform

Daniel Alpay; Alon Kipnis

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arXiv · 1109.1099

Stochastic integration for a wide class of Gaussian stationary increment processes using an extension of the S-transform

Daniel Alpay·Alon Kipnis

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Abstract

Given a Gaussian stationary increment processes with spectral density, we show that a Wick-Ito integral with respect to this process can be naturally obtained using 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 Ito formula.

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Daniel Alpay, Alon Kipnis. 2011-09-06. Stochastic integration for a wide class of Gaussian stationary increment processes using an extension of the S-transform. https://arxiv.org/abs/1109.1099

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