Geodesic
On the theory of stochastic equations in components of semimartingales
Sbornik. Mathematics, Tome 38 (1981) no. 3, pp. 381-394 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The first part of the paper is devoted to the proof of the existence and uniqueness of strong solutions of stochastic equations in components of semimartingales with coefficients depending on the whole past. In the second part variants of the comparison theorem are obtained for strong solutions of stochastic equations in semimartingales. Bibliography: 16 titles. 
@article{SM_1981_38_3_a3,
     author = {A. V. Melnikov},
     title = {On the theory of stochastic equations in components of semimartingales},
     journal = {Sbornik. Mathematics},
     pages = {381--394},
     year = {1981},
     volume = {38},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1981_38_3_a3/}
}
TY  - JOUR
AU  - A. V. Melnikov
TI  - On the theory of stochastic equations in components of semimartingales
JO  - Sbornik. Mathematics
PY  - 1981
SP  - 381
EP  - 394
VL  - 38
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1981_38_3_a3/
LA  - en
ID  - SM_1981_38_3_a3
ER  - 
%0 Journal Article
%A A. V. Melnikov
%T On the theory of stochastic equations in components of semimartingales
%J Sbornik. Mathematics
%D 1981
%P 381-394
%V 38
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1981_38_3_a3/
%G en
%F SM_1981_38_3_a3
A. V. Melnikov. On the theory of stochastic equations in components of semimartingales. Sbornik. Mathematics, Tome 38 (1981) no. 3, pp. 381-394. http://geodesic.mathdoc.fr/item/SM_1981_38_3_a3/

[1] L. I. Galchuk, “O suschestvovanii i edinstvennosti resheniya dlya stokhasticheskikh uravnenii po polumartingalam”, Teoriya veroyatn., XXIII:4 (1978), 782–795 | MR

[2] K. Ito, M. Nisio, “On stationary solutions of stochastic differential equations”, J. Math. Kyoto Univ., 4 (1964), 1–79 | MR

[3] P. Sh. Liptser, A. N. Shiryaev, Statistika sluchainykh protsessov, izd-vo “Nauka”, Moskva, 1974 | MR

[4] I. I. Gikhman, I. I. Kadyrova, “Nekotorye rezultaty issledovaniya stokhasticheskikh differentsialnykh uravnenii”, Teoriya sluchainykh protsessov, izd-vo Naukova Dumka, Kiev, 1973, 51–68

[5] M. Metivier, J. Pellaumail, “Sur une équation stochastique assez générarle”, C. r. Acad. scient. Paris, 285 (197), A 921–A 923 | MR | Zbl

[6] B. S. Tsirelson, “Primer stokhasticheskogo uravneniya, ne imeyuschego silnogo resheniya”, Teoriya veroyatn., XX:2 (1975), 427–430

[7] C. Doleans-Dade, “On the existence and unicity of solutions of stochastic integral equations”, Z. W.-theorie, 36:2 (1976), 93–101 | MR | Zbl

[8] A. V. Skorokhod, Issledovaniya po teorii sluchainykh protsessov, izd-vo Kievskogo un-ta, Kiev, 1961

[9] T. Yamada, “On comparison theorem for solutions of stochastic differential equations and its applications”, J. Math. Kyoto Univ., 13 (1973), 497–512 | MR | Zbl

[10] H. Doss, E. Lenglart, “Sur le comportement asymptotique des solutions d'equations différentielles stochastiques”, C. r. Acad. scient. Paris, 284 (1977), A971–A974 | MR

[11] Yu. M. Kabanov, R. Sh. Liptser, A. N. Shiryaev, “Absolyutnaya nepreryvnost i singulyarnost”, Matem. sb., 107(149) (1978), 364–415 | MR | Zbl

[12] K. Dellasheri, Emkosti i sluchainye protsessy, izd-vo “Mir”, Moskva, 1975 | MR

[13] J. Jacod, “Multivariate point process: predictable projection, Radon–Nicodym derivatives, representation of martingales”, Z. W-theorie, 31:3 (1975), 235–253 | MR | Zbl

[14] P. A. Meyer, “Un cours sur les intégrates stochastiques”, Lecture Notes in Math., 511 (1976), 245–400 | DOI | MR | Zbl

[15] I. I. Gikhman, A. V. Skorokhod, Stokhasticheskie differentsialnye uravneniya, izd-vo “Naukova Dumka”, Kiev, 1968

[16] D. Lepingle, “Sur le comportement asymptotique des martingales locales”, Lecture Notes in Math., 649 (1978), 148–161 | DOI | MR | Zbl