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Teoriya Veroyatnostei i ee Primeneniya, 2023, Volume 68, Issue 1, Pages 106–132
DOI: https://doi.org/10.4213/tvp5489 (Mi tvp5489) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Series expansions of fractional Brownian motions and strong local nondeterminism of bifractional Brownian motions on balls and spheres

T. Lua, Ch. Maa, F. Wangb

a Department of Mathematics, Statistics, and Physics, Wichita State University, Wichita, KS, USA
b Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA, USA
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DOI: https://doi.org/10.4213/tvp5489
Abstract: This paper provides series expansions for fractional Brownian motions on the unit ball and the unit sphere by means of ultraspherical polynomials and spherical harmonics. It establishes the property of strong local nondeterminism of isotropic Gaussian random fields on the unit sphere and that of fractional and bifractional Brownian motions on the unit ball and the unit sphere.
Keywords: conditionally negative definiteness, distance function on the ball, spherical harmonics, trifractional Brownian motion, ultraspherical polynomial.
Received: 20.03.2020
Revised: 16.07.2021
Accepted: 31.08.2021
English version:
Theory of Probability and its Applications, 2023, Volume 68, Issue 1, Pages 88–110
DOI: https://doi.org/10.1137/S0040585X97T991301
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: T. Lu, Ch. Ma, F. Wang, “Series expansions of fractional Brownian motions and strong local nondeterminism of bifractional Brownian motions on balls and spheres”, Teor. Veroyatnost. i Primenen., 68:1 (2023), 106–132; Theory Probab. Appl., 68:1 (2023), 88–110
Citation in format AMSBIB
\Bibitem{LuMaWan23}
\by T.~Lu, Ch.~Ma, F.~Wang
\paper Series expansions of fractional Brownian motions and strong local nondeterminism of bifractional Brownian motions on balls and spheres
\jour Teor. Veroyatnost. i Primenen.
\yr 2023
\vol 68
\issue 1
\pages 106--132
\mathnet{http://mi.mathnet.ru/tvp5489}
\crossref{https://doi.org/10.4213/tvp5489}
\transl
\jour Theory Probab. Appl.
\yr 2023
\vol 68
\issue 1
\pages 88--110
\crossref{https://doi.org/10.1137/S0040585X97T991301}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85166193288}
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  • https://doi.org/10.4213/tvp5489
  • https://www.mathnet.ru/eng/tvp/v68/i1/p106
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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