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.
We obtain necessary and sufficient conditions in order that a Gaussian process of many parameters (more generally, a generalized Gaussian random field in ) 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.
@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}, pages = {143--167}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {24}, number = {2}, year = {1974}, doi = {10.5802/aif.509}, zbl = {0275.60054}, mrnumber = {53 #9362}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.509/} }
TY - JOUR AU - Kallianpur, G. AU - Mandrekar, V. TI - The Markov property for generalized gaussian random fields JO - Annales de l'Institut Fourier PY - 1974 DA - 1974/// SP - 143 EP - 167 VL - 24 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.509/ UR - https://zbmath.org/?q=an%3A0275.60054 UR - https://www.ams.org/mathscinet-getitem?mr=53 #9362 UR - https://doi.org/10.5802/aif.509 DO - 10.5802/aif.509 LA - en ID - AIF_1974__24_2_143_0 ER -
Kallianpur, G.; Mandrekar, V. The Markov property for generalized gaussian random fields. Annales de l'Institut Fourier, Tome 24 (1974) no. 2, pp. 143-167. doi : 10.5802/aif.509. http://www.numdam.org/articles/10.5802/aif.509/
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