This article is cited in 6 papers

On the Erdős–Rényi Partial Sums: Large Deviations, Conditional Behavior

M. V. Kozlov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

Received: 16.11.2000

DOI: 10.4213/tvp3794

 English version: Theory of Probability and its Applications, 2002, 46:4, 636–651

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