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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
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
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
Linking options:
https://www.mathnet.ru/eng/tvp5489https://doi.org/10.4213/tvp5489 https://www.mathnet.ru/eng/tvp/v68/i1/p106
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Abstract page: | 116 | Full-text PDF : | 8 | References: | 38 | First page: | 9 |
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