A generalisation of the fractional Brownian field based on non-Euclidean norms

Molchanov, Ilya; Ralchenko, Kostiantyn (2015). A generalisation of the fractional Brownian field based on non-Euclidean norms. Journal of mathematical analysis and applications, 430(1), pp. 262-278. Elsevier 10.1016/j.jmaa.2015.04.085

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We explore a generalisation of the L´evy fractional Brownian field on the Euclidean space based on replacing the Euclidean norm with another norm. A characterisation result for admissible norms yields a complete description of all self-similar Gaussian random fields with stationary increments. Several integral representations of the introduced random fields are derived. In a similar vein, several non-Euclidean variants of the fractional Poisson field are introduced and it is shown that they share the covariance structure with the fractional Brownian field and converge to it. The shape parameters of the Poisson and Brownian variants are related by convex geometry transforms, namely the radial pth mean body and the polar projection transforms.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Molchanov, Ilya and Ralchenko, Kostiantyn

Subjects:

300 Social sciences, sociology & anthropology > 360 Social problems & social services
500 Science > 510 Mathematics

ISSN:

0022-247X

Publisher:

Elsevier

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

28 Oct 2015 14:22

Last Modified:

08 Aug 2016 15:51

Publisher DOI:

10.1016/j.jmaa.2015.04.085

ArXiv ID:

1410.2523

BORIS DOI:

10.7892/boris.72281

URI:

https://boris.unibe.ch/id/eprint/72281

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