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On representations and simulation of conditioned random walks on integer lattices. / Sakhanenko, A.; Foss, S.

In: Siberian Electronic Mathematical Reports, Vol. 18, No. 2, 51, 2021, p. 1556-1571.

Research output: Contribution to journal › Article › peer-review

Harvard

Sakhanenko, A & Foss, S 2021, 'On representations and simulation of conditioned random walks on integer lattices', Siberian Electronic Mathematical Reports, vol. 18, no. 2, 51, pp. 1556-1571. https://doi.org/10.33048/SEMI.2021.18.116

APA

Sakhanenko, A., & Foss, S. (2021). On representations and simulation of conditioned random walks on integer lattices. Siberian Electronic Mathematical Reports, 18(2), 1556-1571. [51]. https://doi.org/10.33048/SEMI.2021.18.116

Vancouver

Sakhanenko A, Foss S. On representations and simulation of conditioned random walks on integer lattices. Siberian Electronic Mathematical Reports. 2021;18(2):1556-1571. 51. doi: 10.33048/SEMI.2021.18.116

Author

Sakhanenko, A. ; Foss, S. / On representations and simulation of conditioned random walks on integer lattices. In: Siberian Electronic Mathematical Reports. 2021 ; Vol. 18, No. 2. pp. 1556-1571.

BibTeX

@article{f48d56ff3d034163a3f4c26ea17b9180,
title = "On representations and simulation of conditioned random walks on integer lattices",
abstract = "We consider a random walk on a multidimensional integer lattice with random bounds on local times. We introduce a family of auxiliary {"}accompanying{"} processes that have regenerative structures and play key roles in our analysis. We obtain a number of representations for the distribution of the random walk in terms of similar distributions of the {"}accompanying{"} processes. Based on that, we obtain representations for the conditional distribution of the random walk, conditioned on the event that it hits a high level before its death. Under more restrictive assumptions a representation of such type has been obtained earlier by the same authors in a recent paper published in the Springer series on Progress in Probability, 77 (2021), where a certain {"}limiting{"} process was used in place of{"}accompanying{"}processes of the present paper.",
keywords = "Accompanying process, Bounded local times, Conditioned random walk, Potential regeneration, Regenerative sequence, Separating levels, Skip-free distributions",
author = "A. Sakhanenko and S. Foss",
note = "Funding Information: Sakhanenko, A., Foss, S., On representations and simulation of conditioned random walks on integer lattices. {\textcopyright} 2021 Sakhanenko A., Foss S. Research is supported by the RSF research grant No. 17-11-01173-Ext. Received October, 28, 2021, published December, 6, 2021. Publisher Copyright: {\textcopyright} 2021 Sakhanenko A., Foss S.",
year = "2021",
doi = "10.33048/SEMI.2021.18.116",
language = "English",
volume = "18",
pages = "1556--1571",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",
number = "2",

}

RIS

TY - JOUR

T1 - On representations and simulation of conditioned random walks on integer lattices

AU - Sakhanenko, A.

AU - Foss, S.

N1 - Funding Information: Sakhanenko, A., Foss, S., On representations and simulation of conditioned random walks on integer lattices. © 2021 Sakhanenko A., Foss S. Research is supported by the RSF research grant No. 17-11-01173-Ext. Received October, 28, 2021, published December, 6, 2021. Publisher Copyright: © 2021 Sakhanenko A., Foss S.

PY - 2021

Y1 - 2021

N2 - We consider a random walk on a multidimensional integer lattice with random bounds on local times. We introduce a family of auxiliary "accompanying" processes that have regenerative structures and play key roles in our analysis. We obtain a number of representations for the distribution of the random walk in terms of similar distributions of the "accompanying" processes. Based on that, we obtain representations for the conditional distribution of the random walk, conditioned on the event that it hits a high level before its death. Under more restrictive assumptions a representation of such type has been obtained earlier by the same authors in a recent paper published in the Springer series on Progress in Probability, 77 (2021), where a certain "limiting" process was used in place of"accompanying"processes of the present paper.

AB - We consider a random walk on a multidimensional integer lattice with random bounds on local times. We introduce a family of auxiliary "accompanying" processes that have regenerative structures and play key roles in our analysis. We obtain a number of representations for the distribution of the random walk in terms of similar distributions of the "accompanying" processes. Based on that, we obtain representations for the conditional distribution of the random walk, conditioned on the event that it hits a high level before its death. Under more restrictive assumptions a representation of such type has been obtained earlier by the same authors in a recent paper published in the Springer series on Progress in Probability, 77 (2021), where a certain "limiting" process was used in place of"accompanying"processes of the present paper.

KW - Accompanying process

KW - Bounded local times

KW - Conditioned random walk

KW - Potential regeneration

KW - Regenerative sequence

KW - Separating levels

KW - Skip-free distributions

UR - http://www.scopus.com/inward/record.url?scp=85124149059&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=47669593

U2 - 10.33048/SEMI.2021.18.116

DO - 10.33048/SEMI.2021.18.116

M3 - Article

AN - SCOPUS:85124149059

VL - 18

SP - 1556

EP - 1571

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 2

M1 - 51

ER -

ID: 35464407