Time-varying vector random fields on the arccos-quasi-quadratic metric space

Juan Du, Chunsheng Ma
Theory of Stochastic Processes
Vol.29 (45), no.1, 2025, pp.24-45
An arccos-quasi-quadratic metric is defined on a subset of ℝ^d+1 such as a sphere, a ball, an ellipsoidal surface, an ellipsoid, a simplex, a conic surface, or a hyperbolic surface, and the corresponding metric space incorporates several important cases in a unified framework that makes possible for us to study metric-dependent random fields on different metric spaces in a unified manner. Over the arccos-quasi-quadratic metric space, this paper constructs a class of time-varying vector random fields via either spherical harmonics or ultraspherical polynomials, and builds up various parametric and semiparametric covariance matrix structures. The extension problem is discussed as well.
DOI: https://doi.org/10.3842/tsp-3696042752-95
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