We study a family of stationary increment Gaussian processes, indexed by time. These processes are determined by certain measures (generalized spectral measures), and our focus here is on the case when the measure is a singular measure. We characterize the processes arising from when is in one of the classes of affine selfsimilar 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 continuous measures. We further obtain an associated Ito formula (see Theorem 8.1).
- Kondratiev and white noise spaces
- Singular measures
- Spectral pairs
- Stationary increment processes
- Weighted symmetric Fock space
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