Geodesic
On the Erd\H os--R\'enyi Partial Sums: Large Deviations, Conditional Behavior
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 4, pp. 678-696

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We obtain the explicit expression for the constant in the asymptotics of large deviations probabilities of increments of random walks (the Erdős–Rényi partial sums) with the Cramer condition. The trajectories of the walks on which the large deviation is realized are described in the form of conditional limit theorems.
Keywords: random walk, large deviation, conditional invariance principle, factorization identity. 
@article{TVP_2001_46_4_a3,
     author = {M. V. Kozlov},
     title = {On the {Erd\H} {os--R\'enyi} {Partial} {Sums:} {Large} {Deviations,} {Conditional} {Behavior}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {678--696},
     publisher = {mathdoc},
     volume = {46},
     number = {4},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_4_a3/}
}
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M. V. Kozlov. On the Erd\H os--R\'enyi Partial Sums: Large Deviations, Conditional Behavior. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 4, pp. 678-696. http://geodesic.mathdoc.fr/item/TVP_2001_46_4_a3/