On the prospective minimum of the random walk conditioned to stay nonnegative
-
Vladimir A. Vatutin
und
Elena E. Dyakonova
Abstract
Let
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≤n Sm be the minimum of the random walk on the interval [r, n]. It is shown that
can have five different expressions, the forms of which depend on the relationships between the parameters r, k and n.
Originally published in Diskretnaya Matematika (2024) 36, №3, 50–79 (in Russian).
Funding statement: This work was supported by the Russian Science Foundation under grant no.24-11-00037 https://rscf.ru/en/project/24-11-00037/
Acknowledgment
In conclusion, we would like to thank an anonymous reviewer for the constructive comments that allow us to improve the presentation of results of the paper.
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On continuants of continued fractions with rational partial quotients
- On linear equivalence of piecewise-linear permutations of the field 𝔽2n
- On the prospective minimum of the random walk conditioned to stay nonnegative
- Limiting behavior of percolation cluster in a multilayered random environment with breakdown
Artikel in diesem Heft
- Frontmatter
- On continuants of continued fractions with rational partial quotients
- On linear equivalence of piecewise-linear permutations of the field 𝔽2n
- On the prospective minimum of the random walk conditioned to stay nonnegative
- Limiting behavior of percolation cluster in a multilayered random environment with breakdown
