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A Class Of Gaussian Processes With Fractional Spectral Measures, Daniel Alpay, Palle Jorgensen, David Levanony

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study a family of stationary increment Gaussian processes, indexed by time. These processes are determined by certain measures σ (generalized spectral measures), and our focus here is on the case when the measure σ is a singular measure. We characterize the processes arising from when σ is in one of the classes of affine self-similar measures. Our analysis makes use of Kondratiev-white noise spaces. With the use of a priori estimates and the Wick calculus, we extend and sharpen (see Theorem 7.1) earlier computations of Ito stochastic integration developed for the special case of stationary increment processes having absolutely …