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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2024, Volume 519, Pages 33–38
DOI: https://doi.org/10.31857/S2686954324050076 (Mi danma562) 		 
MATHEMATICS

Study of the bias of $N$-particle estimates of the Monte Carlo method in problems with particle interaction

G. A. Mikhailovab, G. Z. Lotovaab, S. V. Rogazinskiiab

a Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
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DOI: https://doi.org/10.31857/S2686954324050076
Abstract: The paper gives a theoretical and numerical justification of the bias with the $O(1/N)$ order for the $N$-particle statistical estimates of the functionals of the solution of nonlinear kinetic equations for the model with interaction of particle trajectories. An estimate of the coefficient in the corresponding bias formula is obtained.
Keywords: chaos propagation hypothesis, Monte Carlo method, Boltzmann equation, rarefied gas theory, SEIR epidemic model, single-particle density distribution, $N$-particle ensemble, $\delta$-continuity, Markov chain.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNM-2022-0002
This work was performed at the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences within the state assignment, project FWNM-2022-0002.
Received: 02.07.2024
Revised: 09.09.2024
Accepted: 19.07.2024
English version:
Doklady Mathematics, 2024, Volume 110, Issue 2, Pages 416–420
DOI: https://doi.org/10.1134/S1064562424601513
Bibliographic databases:
Document Type: Article
UDC: 519.676
Language: Russian
Citation: G. A. Mikhailov, G. Z. Lotova, S. V. Rogazinskii, “Study of the bias of $N$-particle estimates of the Monte Carlo method in problems with particle interaction”, Dokl. RAN. Math. Inf. Proc. Upr., 519 (2024), 33–38; Dokl. Math., 110:2 (2024), 416–420
Citation in format AMSBIB
\Bibitem{MikLotRog24}
\by G.~A.~Mikhailov, G.~Z.~Lotova, S.~V.~Rogazinskii
\paper Study of the bias of $N$-particle estimates of the Monte Carlo method in problems with particle interaction
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2024
\vol 519
\pages 33--38
\mathnet{http://mi.mathnet.ru/danma562}
\crossref{https://doi.org/10.31857/S2686954324050076}
\elib{https://elibrary.ru/item.asp?id=75994113}
\transl
\jour Dokl. Math.
\yr 2024
\vol 110
\issue 2
\pages 416--420
\crossref{https://doi.org/10.1134/S1064562424601513}
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