Using the white noise space framework, we define a class of stochastic processes which include as a particular case the fractional Brownian motion and its derivative. The covariance functions of these processes are of a special form, studied by Schoenberg, von Neumann and Krein.
D. Alpay, H. Attia and D. Levanony. On the characteristics of a class of Gaussian processes within the white noise space setting. Stochastic Processes and their Applications, vol. 120 (issue 7), pp. 1074-1104 (2010).
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NOTICE: this is the author’s version of a work that was accepted for publication in Stochastic Processes and their Applications. 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 Stochastic Processes and their Applications, volume 120, issue 7, in 2010. DOI: 10.1016/j.spa.2010.03.004
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