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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