Geodesic
Small deviations in the sample function space
Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 4, pp. 755-765

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Let $\xi_1\xi_2,\dots$ be a sequence of independent identically distributed random variables and let $$ \mathbf P(\xi_1+\dots+\xi_n(n))\Rightarrow F_\alpha(x) $$ where $F_\alpha(x)$ is a strong stable distribution function. Asymptotic properties (in the region of small deviations) of the logarithmic probability for sample paths of a random walk generated by sums of $\xi_n$ to belong to a given set in $D(0,1)$ are under investigation. 
@article{TVP_1974_19_4_a6,
     author = {A. A. Mogul'skii},
     title = {Small deviations in the sample function space},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {755--765},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1974_19_4_a6/}
}
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A. A. Mogul'skii. Small deviations in the sample function space. Teoriâ veroâtnostej i ee primeneniâ, Tome 19 (1974) no. 4, pp. 755-765. http://geodesic.mathdoc.fr/item/TVP_1974_19_4_a6/