A class of Gaussian processes with fractional spectral measures |
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Authors: | Daniel Alpay Palle Jorgensen |
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Institution: | a Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be?er Sheva 84105, Israel b Department of Mathematics, 14 MLH, The University of Iowa, Iowa City, IA 52242-1419, USA c Department of Electrical Engineering, Ben Gurion University of the Negev, P.O.B. 653, Be?er Sheva 84105, Israel |
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Abstract: | 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 σ when σ 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). |
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Keywords: | Stationary increment processes Weighted symmetric Fock space Kondratiev and white noise spaces Spectral pairs Singular measures |
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