Geodesic
On absolute continuity and singularity of the distributions of random fields
Sbornik. Mathematics, Tome 46 (1983) no. 2, pp. 161-170 
A. A. Gushchin. On absolute continuity and singularity of the distributions of random fields. Sbornik. Mathematics, Tome 46 (1983) no. 2, pp. 161-170. http://geodesic.mathdoc.fr/item/SM_1983_46_2_a1/
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     author = {A. A. Gushchin},
     title = {On absolute continuity and singularity of the distributions of random fields},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A criterion is obtained for the absolute continuity or singularity of probability measures corresponding to certain classes of two-parameter discrete random fields. The proof is based on some lemmas which describe the sets of convergence of two-parameter semimartingales. Bibliography: 5 titles.

[1] Kabanov Yu. M., Liptser R. Sh., Shiryaev A. N., “K voprosu ob absolyutnoi nepreryvnosti i singulyarnosti veroyatnostnykh mer”, Matem. sb., 104 (146) (1977), 227–247 | MR | Zbl

[2] Rozanov Yu. A., Markovskie sluchainye polya, Nauka, M., 1981 | MR | Zbl

[3] Cairoli R., Une inégalité'pour martingales à indices multiples et ses applications, V. 124 (Séminaire de Probabilités IV), Lecture Notes Math., Springer-Verlag, 1970 | MR

[4] Cairoli R., Décomposition de processus à indices doubles, V. 191 (Séminaire de Probabilités V), Lecture Notes Math., Springer-Verlag | MR

[5] Maniya M. G., “Ob absolyutnoi nepreryvnosti i singulyarnosti veroyatnostnykh raspredelenii sluchainykh polei”, DAN SSSR, 253:3 (1980), 530–533 | MR