Summary
Gaussian processes satisfying Osterwalder-Schrader positivity are studied. A representation of the (generalized) covariance function of an OS-positive process as the Laplace transform of an operator-valued probability measure is given. It is shown that every Gaussian OS-positive process has a unique Gaussian canonical Markov extension. An explicit application is made to the generalized free Euclidean fields.
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Partially supported by the National Science Foundation under grant MCS-76 06332
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Klein, A. Gaussian OS-positive processes. Z. Wahrscheinlichkeitstheorie verw Gebiete 40, 115–124 (1977). https://doi.org/10.1007/BF00532876
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DOI: https://doi.org/10.1007/BF00532876