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MARKOV PROPERTY AND COKERNELS OF LOCAL OPERATORS

Published online by Cambridge University Press:  01 December 1997

KOICHIRO IWATA  and
JÖRG SCHÄFER
KOICHIRO IWATA
Affiliation:
Department of Mathematics, Hiroshima University, Higashi-Hiroshima 739, Japan. E-mail: [email protected]
JÖRG SCHÄFER
Affiliation:
Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany. E-mail: [email protected]
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Abstract

We discuss Gaussian generalized random fields indexed by smooth sections of vector bundles with respect to Markov properties. We propose a new set-up which is suitable for the present question and within which new phenomena are detected naturally. In particular, we give a counterexample to the belief that locality in the RKHS implies the germ Markov property. We also prove the close connection between the Markov property and cokernels of local operators. Furthermore, we prove the Markov property for a very degenerate Gaussian random field.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 56 , Issue 3 , December 1997 , pp. 657 - 672
Copyright
The London Mathematical Society 1997

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