Geodesic
Boundary problems for random walks and large deviations in functional spaces
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 4, pp. 635-654

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Asymptotic properties (in the region of large deviations) of the logarithmic probability that the sample paths of a random walk generated by sums of independent addends or by a Poisson process belong to a given open set in $C(0,1)$ or $D(0,1)$ are under consideration. 
@article{TVP_1967_12_4_a3,
     author = {A. A. Borovkov},
     title = {Boundary problems for random walks and large deviations in functional spaces},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {635--654},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_4_a3/}
}
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A. A. Borovkov. Boundary problems for random walks and large deviations in functional spaces. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 4, pp. 635-654. http://geodesic.mathdoc.fr/item/TVP_1967_12_4_a3/