Invariances of random elds paths, with applications in
David Ginsbourger, Olivier Roustant, Nicolas Durrande · 2013
We study pathwise invariances of centred random elds that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path properties including additivity boil down to invariances of the covariance kernel. These results are extended to a broader class of operators in the Gaussian case, via the Lo eve isometry. Several covariance-driven pathwise invariances are illustrated, including elds with symmetric paths, centred paths, har