This article is cited in 53 papers

Small deviations in the sample function space

A. A. Mogul'skii

Novosibirsk

Abstract: Let $\xi_1\xi_2,\dots$ be a sequence of independent identically distributed random variables and let
$$ \mathbf P(\xi_1+\dots+\xi_n<xB(n))\Rightarrow F_\alpha(x) $$
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.

Received: 26.12.1973

 English version: Theory of Probability and its Applications, 1975, 19:1, 726–736

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