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 inJournal of mathematical sciences (New York, N.Y.) Vol. 266; no. 6; pp. 850 - 868
Main Author Afanasyev, V. I.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2022
Springer
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Random processes
Random walk
Conditional random walks
Conditional Brownian motions
Functional limit theorems
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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