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math.PR2014
Wiener-Chaos Approach to Optimal Prediction
Daniel Alpay, Alon Kipnis
The chaos expansion of a general non-linear function of a Gaussian stationary increment process conditioned on its past realizations is derived. This work combines Wiener chaos exp…
math.PR2011
Stochastic integration for a wide class of Gaussian stationary increment processes using an extension of the S-transform
Daniel Alpay, Alon Kipnis
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 no…