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On the prospective minimum of the random walk conditioned to stay nonnegative.
On the prospective minimum of the random walk conditioned to stay nonnegative.
- Source :
-
Discrete Mathematics & Applications . Dec2024, Vol. 34 Issue 6, p337-362. 26p. - Publication Year :
- 2024
-
Abstract
- Let S 0 = 0 , S n = X 1 + ... + X n , n ≥ 1 , be a random walk whose increments belong without centering to the domain of attraction of a stable law with scaling constants an that provide convergence as n → ∞ of the distributions of the sequence {Sn/an, n = 1, 2, ...} to this stable law. Let Lr,n = minr≤m≤nSm be the minimum of the random walk on the interval [r, n]. It is shown that lim r , k , n → ∞ P L r , n ≤ y a k | S n ≤ t a k , L 0 , n ≥ 0 , t ∈ 0 , ∞ , can have five different expressions, the forms of which depend on the relationships between the parameters r, k and n. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09249265
- Volume :
- 34
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 181547307
- Full Text :
- https://doi.org/10.1515/dma-2024-0030