The Markov property for generalized gaussian random fields
Annales de l'Institut Fourier, Volume 24 (1974) no. 2, p. 143-167

We obtain necessary and sufficient conditions in order that a Gaussian process of many parameters (more generally, a generalized Gaussian random field in R n ) possess the Markov property relative to a class of open sets. The method adopted is the Hilbert space approach initiated by Cartier and Pitt. Applications are discussed.

Nous obtenons des conditions nécessaires et suffisantes pour qu’un processus gaussien (ou, plus généralement, une distribution aléatoire gaussienne) à plusieurs paramètres possède la propriété markovienne par rapport à la famille des ensembles ouverts.

@article{AIF_1974__24_2_143_0,
     author = {Kallianpur, G. and Mandrekar, V.},
     title = {The Markov property for generalized gaussian random fields},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {24},
     number = {2},
     year = {1974},
     pages = {143-167},
     doi = {10.5802/aif.509},
     zbl = {0275.60054},
     mrnumber = {53 \#9362},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1974__24_2_143_0}
}

Kallianpur, G.; Mandrekar, V. The Markov property for generalized gaussian random fields. Annales de l'Institut Fourier, Volume 24 (1974) no. 2, pp. 143-167. doi : 10.5802/aif.509. http://www.numdam.org/item/AIF_1974__24_2_143_0/

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