Equivalence problems for Gaussian multiple Markov processes and their canonical representations

Hiroshi Muraoka

Stochastic Processes and their Applications, 1992, vol. 42, issue 2, 291-306

Abstract: We obtain a necessary and sufficient condition for two given Gaussian multiple Markov processes to be equivalent. In case they are equivalent, the Radon-Nikodym density can be expressed in terms of the kernels of their canonical representations. As a development, equivalence of two random fields is discussed assuming that they are in a certain class of isotropic Gaussian fields. It is further shown that such an approach is successful for N-ple Markov Gaussian processes with multiplicity N (N [greater-or-equal, slanted] 1) within our framework.

Keywords: canonical; (Lévy-Hida); representation; multiple; Markov; process; equivalence; of; Gaussian; processes; Radon-Nikodym; density; isotropic; Gaussian; Markov; random; field; Goursat; representation (search for similar items in EconPapers)
Date: 1992
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