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

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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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     author = {R. Sh. Liptser and A. N. Shiryaev},
     title = {On weak convergence of semimartingales to stochastically continuous processes with independent and conditionally independent increments},
     journal = {Sbornik. Mathematics},
     pages = {299--323},
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     volume = {44},
     number = {3},
     year = {1983},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1983_44_3_a4/}
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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/