Document Type
Article
Publication Date
2011
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 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 continuous measures. We further obtain an associated Ito formula (see Theorem 8.1).
Recommended Citation
D. Alpay, P. Jorgensen and D. Levanony. A class of Gaussian processes with fractional spectral measures. Journal of Functional Analysis, Volume 261 (2011), pp. 507-541.
Peer Reviewed
1
Copyright
Elsevier
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Included in
Algebra Commons, Discrete Mathematics and Combinatorics Commons, Other Mathematics Commons
Comments
NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, volume 261, in 2011. DOI: 10.1016/j.jfa.2011.03.012
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