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Markov Property and Cokernels of Local Operators
Author(s) -
Iwata Koichiro,
Schäfer Jörg
Publication year - 1997
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610797005565
Subject(s) - markov chain , markov property , mathematics , counterexample , property (philosophy) , markov kernel , locality , gaussian , connection (principal bundle) , pure mathematics , markov process , random field , variable order markov model , discrete mathematics , markov model , statistics , physics , philosophy , linguistics , geometry , epistemology , quantum mechanics
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.