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Gauss-Markov random fields (CMrf) with continuous indices

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2 Author(s)
Moura, J.M.F. ; Dept. of Electr. & Comput. Eng., Carnegie Mellon Univ., Pittsburgh, PA, USA ; Goswami, S.

Gauss-Markov random fields (GMrfs) play an important role in the modeling of physical phenomena. The paper addresses the second-order characterization and the sample path description of GMrf's when the indexing parameters take values in bounded subsets of ℜd, d⩾1. Using results of Pitt (1994), we give conditions for the covariance of a GMrf to be the Green's function of a partial differential operator and, conversely, for the Green's function of an operator to be the covariance of a GMrf. We then develop a minimum mean square error representation for the field in terms of a partial differential equation driven by correlated noise. The paper establishes for GMrf's on ℜd second-order characterizations that parallel the corresponding results for GMrf's on finite lattices

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Information Theory, IEEE Transactions on  (Volume:43 ,  Issue: 5 )