A class of Gaussian processes with fractional spectral measures
By Daniel Alpay, Palle E. T. Jorgensen, David Levanony. Journal of Functional Analysis, 2010
58 citations recorded by the source corpus.
We study a family of stationary increment Gaussian processes, indexed by time. These processes are determined by certain measures sigma (generalized spectral measures), and our focus here is on the case when the measure sigma is a singular measure. We characterize the processes arising from when sigma 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 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.
Subfields: Applied Mathematics, Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8fdac8a612c1fb264ba3fdb10ef8de875e1db5ff
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Citations in the corpus
- Spectral Theory for Gaussian Processes: Reproducing Kernels, Boundaries, and L2-Wavelet Generators with Fractional Scales (2015, methodology): “We now explain the connections between the present construction and the processes we built in earlier articles [4, 5].”
- On Free Stochastic Processes and their Derivatives (2013, unknown): “where σ is a positive measure satisfying: For this family of Gaussian processes, typically having singular generating measures, we established in [2, 3, 5, 4] a versatile extension of Ito calculus to allow for measures not considered in the traditional family of Gaussian processes.”
- Stochastic Processes Induced by Singular Operators (2011, background): “Still for n = 1, the papers [1, 2] can be seen as the beginning of such a study, for certain absolutely continuous measures, and for certain singular measures respectively.”