Geodesic
Limit theorems for stochastic processes stopped at random
Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 3, pp. 567-569 
D. Szász. Limit theorems for stochastic processes stopped at random. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 3, pp. 567-569. http://geodesic.mathdoc.fr/item/TVP_1971_16_3_a16/
@article{TVP_1971_16_3_a16,
     author = {D. Sz\'asz},
     title = {Limit theorems for stochastic processes stopped at random},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {567--569},
     year = {1971},
     volume = {16},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_3_a16/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Convergence of distributions of stochastic processes stopped at random is investigated in case when the stopping time does not depend on the processes in question. A necessary condition and, in case of processes with independent increments, a sufficient condition are given. The results can be applied to sums of a random number of independent random variables.