LOCAL INVARIANCE PRINCIPLE FOR A RANDOM WALK WITH ZERO DRIFT

We consider a random walk S n , n ≥ 0 with zero drift and finite variance σ 2 . Let T be the first hitting time of the semi-axis - ∞ , 0 by this random walk. For the random process S n t / σ n , t ∈ 0 , 1 , considered under the condition that T = n , a functional limit theorem on its convergence to...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022-10, Vol.266 (6), p.850-868
Main Author: Afanasyev, V. I.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Random processes
Random walk
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Summary:We consider a random walk S n , n ≥ 0 with zero drift and finite variance σ 2 . Let T be the first hitting time of the semi-axis - ∞ , 0 by this random walk. For the random process S n t / σ n , t ∈ 0 , 1 , considered under the condition that T = n , a functional limit theorem on its convergence to the Brownian excursion, as n → ∞ , is proved.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-06145-8