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

Daniel Alpay; David Levanony

doi:10.1007/s11118-007-9070-4

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

Daniel Alpay, David Levanony

Department of Electrical & Computer Engineering

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

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.

Original language	English
Pages (from-to)	163-184
Number of pages	22
Journal	Potential Analysis
Volume	28
Issue number	2
DOIs	https://doi.org/10.1007/s11118-007-9070-4
State	Published - 1 Mar 2008

Keywords

Bi-fractional Brownian motion
Reproducing kernel Hilbert spaces

ASJC Scopus subject areas

Analysis

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10.1007/s11118-007-9070-4

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title = "On the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions",

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.",

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AU - Levanony, David

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N2 - 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.

AB - 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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EP - 184

JO - Potential Analysis

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

Abstract

Keywords

ASJC Scopus subject areas

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