On the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions

Mathematics – Probability

Scientific paper

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Scientific paper

We present decompositions of various positive kernels as integrals or sums of
positive kernels. Within this framework we study the reproducing kernel Hilbert
spaces associated with the fractional and bi-fractional Brownian motions. As a
tool, we define a new function of two complex variables, which is a natural
generalization of the classical Gamma function for the setting we consider

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