Geodesic
Limit theorems for stopped random sequences.~I: Rates of convergence and asymptotic expansions
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 4, pp. 800-826

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Stopped random sequences with record regeneration are considered and limit theorems refining the normal approximation are proved. Particular cases of such sequences are stopped random walks, recurrent Markov renewal processes, and certain procedures of sequential estimation.
Keywords: stopped random sequences, asymptotic expansions, record regeneration. 
@article{TVP_1993_38_4_a5,
     author = {V. K. Malinovskii},
     title = {Limit theorems for stopped random {sequences.~I:} {Rates} of convergence and asymptotic expansions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {800--826},
     publisher = {mathdoc},
     volume = {38},
     number = {4},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_4_a5/}
}
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V. K. Malinovskii. Limit theorems for stopped random sequences.~I: Rates of convergence and asymptotic expansions. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 4, pp. 800-826. http://geodesic.mathdoc.fr/item/TVP_1993_38_4_a5/