Detection of Gauss-Markov random fields with nearest-neighbor dependency
IEEE Transactions on Information Theory
Recursive filtering and smoothing for Gaussian reciprocal processes with continuous indices
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
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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