Stochastic integration for a wide class of Gaussian stationary increment processes using an extension of the S-transform
Probability
2012-02-09 v3
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.
Keywords
Cite
@article{arxiv.1109.1099,
title = {Stochastic integration for a wide class of Gaussian stationary increment processes using an extension of the S-transform},
author = {Daniel Alpay and Alon Kipnis},
journal= {arXiv preprint arXiv:1109.1099},
year = {2012}
}
Comments
Improved version