Geodesic
On weak convergence of semimartingales to stochastically continuous processes with independent and conditionally independent increments
Sbornik. Mathematics, Tome 44 (1983) no. 3, pp. 299-323 Cet article a éte moissonné depuis la source Math-Net.Ru

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The authors study weak convergence of a sequence of semimartingales to an arbitrary stochastically continuous process independent or conditionally independent increments. The “semimartingale scheme” they consider includes the traditional “series scheme”. Bibliography: 22 titles. 
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     title = {On weak convergence of semimartingales to stochastically continuous processes with independent and conditionally independent increments},
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R. Sh. Liptser; A. N. Shiryaev. On weak convergence of semimartingales to stochastically continuous processes with independent and conditionally independent increments. Sbornik. Mathematics, Tome 44 (1983) no. 3, pp. 299-323. http://geodesic.mathdoc.fr/item/SM_1983_44_3_a4/

[1] Liptser R. Sh., Shiryaev A. N., “Funktsionalnaya tsentralnaya predelnaya teorema dlya semimartingalov”, Teoriya veroyatn., XXV:4 (1980), 683–703 | MR | Zbl

[2] Liptser R. Sh., Shiryaev A. N., “O neobkhodimykh i dostatochnykh usloviyakh v funktsionalnoi tsentralnoi predelnoi teoreme”, Teoriya veroyatn., XXVI:1 (1981), 132–137 | MR | Zbl

[3] Kabanov Yu., Liplser R., Shiryayev A., “Some limit theorem for simple point processes (martingale approach)”, Stochastics, 3:3 (1980), 203–216 | MR | Zbl

[4] Jacod J., Memin J., “Sur la convergence des semimartingales, vers un processus á accoroisement indépendants”, Lecture Notes in Math., 784, Springer-Verlag, 1980, 227–248 | MR

[5] Gnedenko B. V., Kolmogorov A. N., Predelnye raspredeleniya dlya summ nezavisimykh sluchainykh velichin, Gostekhizdat, M., L., 1949

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

[7] Jacod J., Calcul stochastique et problèmes de martingales, Lecture Notes in Math., 714, Springer-Verlag, 1979 | MR | Zbl

[8] Helland I. S., “On weak convergence to Brownian motion”, W-theorie, 52:3 (1980), 251–265 | MR | Zbl

[9] Skorokhod A. V., Sluchainye protsessy s nezavisimymi prirascheniyami, Nauka, M., 1964 | MR | Zbl

[10] Rebolledo R., “Central limit theorem for local martingales”, W-theorie, 51:3 (1980), 269–286 | MR | Zbl

[11] Brown T., “A martingale approach to the Poisson convergence of simple point processes”, Ann. Prob., 6 (1978), 615–628 | DOI | MR | Zbl

[12] Brown T., Compensators and Cox convergence, Preprint, 1980

[13] Klopotowsky A., “Mixtures of infinitely divisible distributions as limit laws for sums of dependent random variables”, W-theorie, 51:1 (1980), 101–113 | MR

[14] Jacod J., Memin J., Un nouveau critere de compacité relative pour une suite de processus, Preprint, 1980

[15] Lenglart E., “Relation de domination entre deux processus”, Ann. Inst. H. Poincaré, Sect. B., XIII (1977), 171–179 | MR

[16] Dellasheri K., Emkosti i sluchainye protsessy, Mir, M., 1975 | MR

[17] Doleans-Dade C., “Quelques applications de la formula changement de variables pour les semimartingales”, W-theorie, 16 (1970), 181–194 | MR | Zbl

[18] Aldous D., “Stopping time and tightness”, Ann. Probab., 6:2 (1978), 335–340 | DOI | MR | Zbl

[19] Rebolledo R., “La méthode des martingales appliquée à l'étude de la convergence en loi de processus”, Bull. Soc. Math. France, Mémoires 62, 1979, 125 | MR | Zbl

[20] Metivier M., “Sufficient conditions for tightness and weak convergence of processes”, Internal Report, MN 55455, School of Math. Univ. of Minnesota, Minneapolis

[21] McLeish D. L., “Dependent central limit theorems and invariance principles”, Ann. Probab., 2:4 (1974), 620–628 | DOI | MR | Zbl

[22] Billingsli P., Skhodimost veroyatnostnykh mer, Nauka, M., 1977 | MR