Abstract
The main difference between our measures on \(\mathbb{R}\), and the measures used in fractional Brownian motion and related processes is that our measures are finite on \(\mathbb{R}\), but the others aren’t; instead they are what is called tempered (see [AL08]). If μ is a tempered positive measure, then the function \(F =\widehat{ d\mu }\) is still positive definite, but it is not continuous, unless \(\mu \left (\mathbb{R}\right ) < \infty \).
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Jorgensen, P., Pedersen, S., Tian, F. (2016). Overview and Open Questions. In: Extensions of Positive Definite Functions. Lecture Notes in Mathematics, vol 2160. Springer, Cham. https://doi.org/10.1007/978-3-319-39780-1_11
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DOI: https://doi.org/10.1007/978-3-319-39780-1_11
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