Geodesic
Large deviations for trajectories of multidimensional random walks
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 2, pp. 309-323

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The paper deals with asymptotic properties (in the region of large deviations) of the logarithmic probability for the sample paths of a random walk, generated by sums of independent random vectors, to belong to a given open set in $C^N(0,1)$. 
@article{TVP_1976_21_2_a6,
     author = {A. A. Mogul'skiǐ},
     title = {Large deviations for trajectories of multidimensional random walks},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {309--323},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_2_a6/}
}
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A. A. Mogul'skiǐ. Large deviations for trajectories of multidimensional random walks. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 2, pp. 309-323. http://geodesic.mathdoc.fr/item/TVP_1976_21_2_a6/