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Multifractional Vector Brownian Motions,Their Decompositions,and Generalizations
Authors:Chunsheng Ma
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
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.
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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