Modelling of random processes and fields based on randomized piecewise constant replenishment of discrete argument processes and Palm flows with summation of their trajectories

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Modelling of random processes and fields based on randomized piecewise constant replenishment of discrete argument processes and Palm flows with summation of their trajectories. / Akenteva, Marina S.; Kargapolova, Nina A.; Ogorodnikov, Vasily A. et al.

In: Russian Journal of Numerical Analysis and Mathematical Modelling, Vol. 41, No. 1, 06.02.2026, p. 1-13.

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

BibTeX

@article{ef3b8f4141b24a5fa8a01f319cfa1b6a,

title = "Modelling of random processes and fields based on randomized piecewise constant replenishment of discrete argument processes and Palm flows with summation of their trajectories",

abstract = "The paper presents a generalization of the well-known method of modelling a continuous argument process based on randomized piecewise constant replenishment of the discrete argument process. It is proposed to additionally summarize the trajectories of a piecewise constant process in the case the distributions of the initial process are infinitely divisible. The behavior of continuous argument processes is studied when the number of terms tends to infinity. The conditions under which the sequence of processes constructed this way weakly converges in the Skorokhod and Lp spaces are presented and the properties of limiting processes are studied. In addition, an algorithm for modelling homogeneous random fields with piecewise constant realizations based on the Palm flows and summation of realizations is proposed.",

keywords = "Skorokhod space, homogeneous field, random process, weak convergence, случайный процесс, однородное поле, слабая сходимость, пространство Скорохода",

author = "Akenteva, {Marina S.} and Kargapolova, {Nina A.} and Ogorodnikov, {Vasily A.} and Shengnan Li",

note = "Modelling of random processes and fields based on randomized piecewise constant replenishment of discrete argument processes and Palm flows with summation of their trajectories / M. S. Akenteva, N. A. Kargapolova, V. A. Ogorodnikov, Sh. Li // Russian Journal of Numerical Analysis and Mathematical Modelling. – 2026. – Vol. 41, No. 1. – P. 1-13. – DOI 10.1515/rnam-2026-0001. – EDN EBWXJG. The research was carried out within the framework of the state assignment of the ICMMG, SB RAS FWNM–2025–0002.",

year = "2026",

month = feb,

day = "6",

doi = "10.1515/rnam-2026-0001",

language = "English",

volume = "41",

pages = "1--13",

journal = "Russian Journal of Numerical Analysis and Mathematical Modelling",

issn = "0927-6467",

publisher = "Walter de Gruyter GmbH",

number = "1",

}

RIS

TY - JOUR

T1 - Modelling of random processes and fields based on randomized piecewise constant replenishment of discrete argument processes and Palm flows with summation of their trajectories

AU - Akenteva, Marina S.

AU - Kargapolova, Nina A.

AU - Ogorodnikov, Vasily A.

AU - Li, Shengnan

N1 - Modelling of random processes and fields based on randomized piecewise constant replenishment of discrete argument processes and Palm flows with summation of their trajectories / M. S. Akenteva, N. A. Kargapolova, V. A. Ogorodnikov, Sh. Li // Russian Journal of Numerical Analysis and Mathematical Modelling. – 2026. – Vol. 41, No. 1. – P. 1-13. – DOI 10.1515/rnam-2026-0001. – EDN EBWXJG. The research was carried out within the framework of the state assignment of the ICMMG, SB RAS FWNM–2025–0002.

PY - 2026/2/6

Y1 - 2026/2/6

N2 - The paper presents a generalization of the well-known method of modelling a continuous argument process based on randomized piecewise constant replenishment of the discrete argument process. It is proposed to additionally summarize the trajectories of a piecewise constant process in the case the distributions of the initial process are infinitely divisible. The behavior of continuous argument processes is studied when the number of terms tends to infinity. The conditions under which the sequence of processes constructed this way weakly converges in the Skorokhod and Lp spaces are presented and the properties of limiting processes are studied. In addition, an algorithm for modelling homogeneous random fields with piecewise constant realizations based on the Palm flows and summation of realizations is proposed.

AB - The paper presents a generalization of the well-known method of modelling a continuous argument process based on randomized piecewise constant replenishment of the discrete argument process. It is proposed to additionally summarize the trajectories of a piecewise constant process in the case the distributions of the initial process are infinitely divisible. The behavior of continuous argument processes is studied when the number of terms tends to infinity. The conditions under which the sequence of processes constructed this way weakly converges in the Skorokhod and Lp spaces are presented and the properties of limiting processes are studied. In addition, an algorithm for modelling homogeneous random fields with piecewise constant realizations based on the Palm flows and summation of realizations is proposed.

KW - Skorokhod space

KW - homogeneous field

KW - random process

KW - weak convergence

KW - случайный процесс

KW - однородное поле

KW - слабая сходимость

KW - пространство Скорохода

UR - https://www.mendeley.com/catalogue/1af28c0e-6ef2-3d99-814d-c99de6848772/

UR - https://www.scopus.com/pages/publications/105030338364

UR - https://elibrary.ru/item.asp?id=90526715

U2 - 10.1515/rnam-2026-0001

DO - 10.1515/rnam-2026-0001

M3 - Article

VL - 41

SP - 1

EP - 13

JO - Russian Journal of Numerical Analysis and Mathematical Modelling

JF - Russian Journal of Numerical Analysis and Mathematical Modelling

SN - 0927-6467

IS - 1

ER -

ID: 85084544