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 Diskr. Mat., 2019, Volume 31, Issue 1, Pages 7–20 (Mi dm1545)

Functional limit theorem for the local time of stopped random walk

V. I. Afanasyev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Integer random walk $\{ S_{n}, n\geq 0\}$ with zero drift and finite variance $\sigma ^{2}$ stopped at the moment $T$ of the first visit to the half axis $( -\infty ,0]$ is considered. For the random process which associates the variable $u\geq 0$ with the number of visits the state $\lfloor u\sigma \sqrt{n}\rfloor$ by this walk conditioned on $T>n$, the functional limit theorem on the convergence to the local time of stopped Brownian meander is proved.

Keywords: conditioned Brownian motions, local time of conditioned Brownian motions, functional limit theorems

DOI: https://doi.org/10.4213/dm1545

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English version:
Discrete Mathematics and Applications, 2020, 30:3, 147–157

Bibliographic databases:

UDC: 519.214.6+519.217.31

Citation: V. I. Afanasyev, “Functional limit theorem for the local time of stopped random walk”, Diskr. Mat., 31:1 (2019), 7–20; Discrete Math. Appl., 30:3 (2020), 147–157

Citation in format AMSBIB
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