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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Fractional Brownian fields over manifolds


Author: Zachary A. Gelbaum
Journal: Trans. Amer. Math. Soc. 366 (2014), 4781-4814
MSC (2010): Primary 60G60, 60G15, 58J35
DOI: https://doi.org/10.1090/S0002-9947-2014-06106-0
Published electronically: April 1, 2014
MathSciNet review: 3217700
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Abstract: Extensions of the fractional Brownian fields are constructed over a complete Riemannian manifold. This construction is carried out for the full range of the Hurst parameter $ \alpha \in (0,1)$. In particular, we establish existence, distributional scaling (self-similiarity), stationarity of the increments, and almost sure Hölder continuity of sample paths. Stationary counterparts to these fields are also constructed.


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Additional Information

Zachary A. Gelbaum
Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331
Email: zachgelbaum@gmail.com

DOI: https://doi.org/10.1090/S0002-9947-2014-06106-0
Received by editor(s): July 26, 2012
Received by editor(s) in revised form: November 17, 2012
Published electronically: April 1, 2014
Dedicated: In loving memory of my grandfather, B.R. Gelbaum
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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