{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:50:54Z","timestamp":1747198254808,"version":"3.40.5"},"reference-count":16,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["23-79-30017"],"award-info":[{"award-number":["23-79-30017"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["075-15-2021-581"],"award-info":[{"award-number":["075-15-2021-581"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>It is well known that shortened modeling of particle trajectories with the use multiplicative statistical weights, as a rule, increases the efficiency of the program (in terms of accuracy\/time ratio).\nThis trick is often used in non-branching schemes simulating transfer processes without multiplication (for example, the transfer of X-ray radiation), in which it is sufficient to confine ourselves to studying only the average values of the field characteristics.\nWith an increase in energy, however, multiplication processes begin to play a significant role (the production of electron-photon pairs by gamma quanta with energies above 1.022\u2009MeV, etc.), when the resulting trajectory is not just a broken curve in the phase space, but a branched tree.\nThis technique is also applicable to this process, but only if the study of statistical fluctuations and correlations is not the purpose of the calculation.\nThe present review contains the basic concepts of the Monte Carlo method as applied to the theory of particle transport, demonstration of the weighting method in non-branching processes, and ends with a discussion of unbiased estimates of the second moment and covariance of additive functionals.<\/jats:p>","DOI":"10.1515\/mcma-2023-2015","type":"journal-article","created":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T17:41:31Z","timestamp":1698082891000},"page":"107-129","source":"Crossref","is-referenced-by-count":0,"title":["A weight Monte Carlo estimation of fluctuations in branching processes"],"prefix":"10.1515","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0594-7610","authenticated-orcid":false,"given":"Vladimir","family":"Uchaikin","sequence":"first","affiliation":[{"name":"Department of Theoretical Physics , Ulyanovsk State University , L. Tolstoy str. 42, 432017 Ulyanovsk , Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9349-0998","authenticated-orcid":false,"given":"Elena","family":"Kozhemiakina","sequence":"additional","affiliation":[{"name":"Department of Theoretical Physics , Ulyanovsk State University , L. Tolstoy str. 42, 432017 Ulyanovsk , Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,10,24]]},"reference":[{"key":"2024052809495369729_j_mcma-2023-2015_ref_001","doi-asserted-by":"crossref","unstructured":"S. M. Ermakov,\nVariance of the simplest Monte Carlo estimators in the sign-changing case,\nMonte Carlo Methods Appl. 17 (2011), no. 4, 411\u2013417.","DOI":"10.1515\/mcma.2011.017"},{"key":"2024052809495369729_j_mcma-2023-2015_ref_002","doi-asserted-by":"crossref","unstructured":"S. M. Ermakov and A. A. Zhiglyavskii,\nThe Monte Carlo method for estimation of functionals of characteristic measures of linear integral operators,\nUSSR Comput. Math. Math. Phys. 25 (1985), no. 3, 15\u201323.","DOI":"10.1016\/0041-5553(85)90068-0"},{"key":"2024052809495369729_j_mcma-2023-2015_ref_003","doi-asserted-by":"crossref","unstructured":"P. Glasserman,\nMonte Carlo Methods in Financial Engineering,\nSpringer, New York, 2004.","DOI":"10.1007\/978-0-387-21617-1"},{"key":"2024052809495369729_j_mcma-2023-2015_ref_004","doi-asserted-by":"crossref","unstructured":"J. Guo,\nThe progress of three astrophysics simulation methods: Monte-Carlo, PIC and MHD,\nJ. Phys. Conf. Ser. 2012\n(2021), no. 1, Article ID 012136.","DOI":"10.1088\/1742-6596\/2012\/1\/012136"},{"key":"2024052809495369729_j_mcma-2023-2015_ref_005","doi-asserted-by":"crossref","unstructured":"B. C. Kiedrowski,\nReview of early 21st-century Monte Carlo perturbation and sensitivity techniques for \ud835\udc58-eigenvalue radiation transport calculations,\nNuclear Science and Engineering, 185 (2017), no. 3, 426\u2013444.","DOI":"10.1080\/00295639.2017.1283153"},{"key":"2024052809495369729_j_mcma-2023-2015_ref_006","unstructured":"A. M. Kolchuzhkin and V. V. Uchaikin,\nIntroduction in the Theory of Particles Penetration through a Matter\n(in Russian),\nAtomizdat, Moscow, 1978."},{"key":"2024052809495369729_j_mcma-2023-2015_ref_007","doi-asserted-by":"crossref","unstructured":"D. P. Kroese, T. Brereton, T. Taimre and Z. I. Botev,\nWhy the Monte Carlo method is so important today,\nWiley Interdiscip. Rev. Comput. Stat. 6 (2014), no. 6,386\u2013392.","DOI":"10.1002\/wics.1314"},{"key":"2024052809495369729_j_mcma-2023-2015_ref_008","unstructured":"G. I. Marchuk, G. A. Mikhailov, M. A. Nazareliev, R. A. Darbinjan, B. A. Kargin and B. S. Elepov,\nThe Monte Carlo Methods in Atmospheric Optics,\nSpringer, Berlin, 2013."},{"key":"2024052809495369729_j_mcma-2023-2015_ref_009","doi-asserted-by":"crossref","unstructured":"G. A. Mikhailov and K. K. Sabelfeld,\nOptimization of Weighted Monte Carlo Methods,\nSpringer, Berlin, 1992.","DOI":"10.1007\/978-3-642-75981-9"},{"key":"2024052809495369729_j_mcma-2023-2015_ref_010","doi-asserted-by":"crossref","unstructured":"C. P. Robert and G. Casella,\nMonte Carlo Statistical Methods,\nSpringer, New York, 2004.","DOI":"10.1007\/978-1-4757-4145-2"},{"key":"2024052809495369729_j_mcma-2023-2015_ref_011","doi-asserted-by":"crossref","unstructured":"K. K. Sabelfeld,\nExpansion of random boundary excitations for some elliptic PDEs,\nMonte Carlo Methods Appl. 13 (2007), no. 5\u20136, 403\u2013451.","DOI":"10.1515\/mcma.2007.022"},{"key":"2024052809495369729_j_mcma-2023-2015_ref_012","doi-asserted-by":"crossref","unstructured":"K. Sabelfeld, I. Shalimova and A. Levykin,\nStochastic simulation method for a 2D elasticity problem with random loads, Probab. Engrg. Mech. 24 (2009), no. 1, 2\u201315.","DOI":"10.1016\/j.probengmech.2007.12.020"},{"key":"2024052809495369729_j_mcma-2023-2015_ref_013","doi-asserted-by":"crossref","unstructured":"K. K. Sabelfeld and N. A. Simonov,\nRandom Walks on Boundary for Solving PDFs,\nVSP, Utrecht, 1994.","DOI":"10.1515\/9783110942026"},{"key":"2024052809495369729_j_mcma-2023-2015_ref_014","doi-asserted-by":"crossref","unstructured":"G. K. Stuart, S. E. Minkoff and F. Pereira,\nA two-stage Markov chain Monte Carlo method for seismic inversion and uncertainty quantification,\nGeophysics, 84 (2019), no. 6, R1003\u2013R1020.","DOI":"10.1190\/geo2018-0893.1"},{"key":"2024052809495369729_j_mcma-2023-2015_ref_015","doi-asserted-by":"crossref","unstructured":"V. V. Uchaikin,\nMonte Carlo simulation of particle transport with multiplication,\nUSSR Comput. Math. Math. Phys. 16 (1976), no. 3, 209\u2013217.","DOI":"10.1016\/0041-5553(76)90216-0"},{"key":"2024052809495369729_j_mcma-2023-2015_ref_016","unstructured":"V. V. Uchaikin,\nElectron-Photon Cascades,\nSpringer, Heidelberg, in press."}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2023-2015\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2023-2015\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,28]],"date-time":"2024-05-28T09:50:10Z","timestamp":1716889810000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2023-2015\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,24]]},"references-count":16,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,10,24]]},"published-print":{"date-parts":[[2024,6,1]]}},"alternative-id":["10.1515\/mcma-2023-2015"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2023-2015","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"type":"print","value":"0929-9629"},{"type":"electronic","value":"1569-3961"}],"subject":[],"published":{"date-parts":[[2023,10,24]]}}}