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Discrete Mathematics and Applications

Editor-in-Chief: Zubkov, Andrei


CiteScore 2016: 0.16

SCImago Journal Rank (SJR) 2016: 0.231
Source Normalized Impact per Paper (SNIP) 2016: 0.552

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1569-3929
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Volume 28, Issue 3

Issues

On the non-recurrent random walk in a random environment

Valeriy I. Afanasyev
Published Online: 2018-06-14 | DOI: https://doi.org/10.1515/dma-2018-0014

Abstract

For weakly transient random walk in a random environment that tend at −∞ the limit theorem for the time of hitting a high level is proved.

Keywords: random walk in a random environment; branching process with migration in a random environment; Brownian excursion; functional limit theorems

Note

Originally published in Diskretnaya Matematika (2016) 28, №4, 6–28 (in Russian).

References

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    Afanasyev V. I., “On the time of attaining a high level by a transient randomwalk in a random environment”, Theory Probab. Appl., 61:2 (2017), 178–207.CrossrefGoogle Scholar

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    Kesten H., Kozlov M.V., Spitzer F., “A limit law for random walk in a random environment”, Compositio mathematica, 30:2 (1975), 145-168.Google Scholar

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    Geiger J., Kersting G., Vatutin V. A., “Limit theorems for subcritical branching processes in random environment”, Ann. Inst. H. PoincareProbab. Statist., 39:4 (2003), 593-620.Google Scholar

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    Afanasyev V. I., Random walks and branching processes, M.: MIAN, 2007.Google Scholar

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    Afanasyev V. I., “About time of reaching a high level by a random walk in a random environment”, Theory Probab. Appl., 57:4 (2013), 547–567.Web of ScienceCrossrefGoogle Scholar

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    Afanasyev V. I., “A new theorem for a critical branching process in random environment”, Discrete Math. Appl., 7:5 (1997), 497–513.Google Scholar

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    Durrett R.T., Iglehart D.L., “Functionals of Brownian meander and Brownian excursion”, Ann. Probab., 5:1 (1977), 130-135.CrossrefGoogle Scholar

About the article

Received: 2017-06-27

Revised: 2017-10-28

Published Online: 2018-06-14

Published in Print: 2018-06-26


This work was supported by the RFBR (grant 14-01-00318) and by the Presidium of RAS program “Mathematical problems of modern control theory”.


Citation Information: Discrete Mathematics and Applications, Volume 28, Issue 3, Pages 139–156, ISSN (Online) 1569-3929, ISSN (Print) 0924-9265, DOI: https://doi.org/10.1515/dma-2018-0014.

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Валерий Иванович Афанасьев and Valeriy Ivanovich Afanasyev
Теория вероятностей и ее применения, 2018, Volume 63, Number 3, Page 417

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