On the Reproducing Kernel Hilbert Spaces Associated with the Fractional and Bi-Fractional Brownian Motions |
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| Authors: | Daniel Alpay David Levanony |
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| Affiliation: | (1) Department of Mathematics, Ben-Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, Israel;(2) Department of Electrical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, Israel |
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| Abstract: | 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. D. Alpay thanks the Earl Katz family for endowing the chair which supports his research. |
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| Keywords: | Bi-fractional Brownian motion Reproducing kernel Hilbert spaces |
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