Multifractional Vector Brownian Motions,Their Decompositions,and Generalizations |
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| Authors: | Chunsheng Ma |
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| Institution: | Department of Mathematics, Statistics, and Physics, Wichita State University, Wichita, Kansas, USA, School of Economics, Wuhan University of Technology, Hubei, P. R. China, and School of Mathematics and Statistics, Hubei Engineering University, Xiaogan, Hubei, P. R. China |
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| Abstract: | This article introduces three types of covariance matrix structures for Gaussian or elliptically contoured vector random fields in space and/or time, which include fractional, bifractional, and trifractional vector Brownian motions as special cases, and reveals the relationships among these vector random fields, with an orthogonal decomposition established for the multifractional vector Brownian motion. |
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| Keywords: | Bifractional Brownian motion Covariance matrix function Cross covariance Direct covariance Elliptically contoured random field Gaussian random field Fractional Brownian motion Schoenberg-Lévy kernel Self-similar Trifactional Brownian motion Variogram |
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