Geodesic
Asymptotic behavior of large deviation probabilities for a~simple oscillating random walk
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 1, pp. 89-94.

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This paper considers simple oscillating random walks with $\tilde{S}_n=\sum\limits^n_{i=1} \tilde{X}_i$, under the assumption that $\mathbf P (\tilde{X}_{n+1}=1\mid \tilde{S}_n>0)=p>1/2$. We show that the asymptotic behavior of probability to reach high level for the oscillating random walk and a standard random walk are similar up to a constant multiplier. The asymptotics for the maximum of a random walk and for the moment of the first exit beyond the high level are obtained. 
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E. L. Vetrova. Asymptotic behavior of large deviation probabilities for a~simple oscillating random walk. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 1, pp. 89-94. http://geodesic.mathdoc.fr/item/FPM_2020_23_1_a4/

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