{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,31]],"date-time":"2024-08-31T00:16:58Z","timestamp":1725063418379},"reference-count":10,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we suggest joint application of computational probabilistic analysis and the Monte Carlo method for numerical stochastic modeling problems.\nWe use all the capabilities of computational probabilistic analysis while maintaining all the advantages of the Monte Carlo method.\nOur approach allows us to efficiently implement a computational hybrid scheme.\nIn this way, we reduce the computation time and present the results in the form of distributions.\nThe crucial new points of our method are arithmetic operations on probability density functions and procedures for constructing on the probabilistic extensions.\nRelying on specific numerical examples of solving systems of linear algebraic equations with random coefficients, we present the advantages of our approach.<\/jats:p>","DOI":"10.1515\/mcma-2024-2006","type":"journal-article","created":{"date-parts":[[2024,6,17]],"date-time":"2024-06-17T15:20:50Z","timestamp":1718637650000},"page":"217-223","source":"Crossref","is-referenced-by-count":0,"title":["Joint application of the Monte Carlo method and computational probabilistic analysis in problems of numerical modeling with data uncertainties"],"prefix":"10.1515","volume":"30","author":[{"given":"Boris","family":"Dobronets","sequence":"first","affiliation":[{"name":"Institute of Space and Information Technology , Siberian Federal University , Krasnoyarsk , Russia"}]},{"given":"Olga","family":"Popova","sequence":"additional","affiliation":[{"name":"Institute of Space and Information Technology , Siberian Federal University , Krasnoyarsk , Russia"}]}],"member":"374","published-online":{"date-parts":[[2024,6,18]]},"reference":[{"key":"2024083008370641169_j_mcma-2024-2006_ref_001","unstructured":"B. Dobronets, A. Krantsevich and N. Krantsevich,\nSoftware implementation of numerical operations on random variables,\nJ. Siberian Federal Univ. Math. Phys. 6 (2013), no. 2, 168\u2013173."},{"key":"2024083008370641169_j_mcma-2024-2006_ref_002","unstructured":"B. S. Dobronets and O. A. Popova,\nNumerical probabilistic analysis under aleatory and epistemic uncertainty,\nReliab. Comput. 19 (2014), 274\u2013289."},{"key":"2024083008370641169_j_mcma-2024-2006_ref_003","doi-asserted-by":"crossref","unstructured":"B. Dobronets and O. Popova,\nComputational aspects of probabilistic extensions,\nTomsk State Univ. J. Control Comput. Sci. 47 (2019), 41\u201348.","DOI":"10.17223\/19988605\/47\/5"},{"key":"2024083008370641169_j_mcma-2024-2006_ref_004","unstructured":"B. S. Dobronets and O. A. Popova,\nComputational Probabilistic Analysis: Models and Methods (in Russian),\nSiberian Federal University, Krasnoyarsk, 2020."},{"key":"2024083008370641169_j_mcma-2024-2006_ref_005","doi-asserted-by":"crossref","unstructured":"G. S. Fishman,\nMonte Carlo: Concepts, Algorithms, and Applications,\nSpringer, New York, 1996.","DOI":"10.1007\/978-1-4757-2553-7"},{"key":"2024083008370641169_j_mcma-2024-2006_ref_006","unstructured":"G. A. Mikhailov and A. V. Voitishek,\nStatistical Modeling. Methods Monte Carlo: Textbook. Manual for Bachelor\u2019s and Master\u2019s Degrees (in Russian),\nYurayt, Moscow, 2018."},{"key":"2024083008370641169_j_mcma-2024-2006_ref_007","unstructured":"R. E. Moore,\nRisk analysis without Monte Carlo methods,\nFreiburger Intervall-Ber. 84\/1 (1984), 1\u201348."},{"key":"2024083008370641169_j_mcma-2024-2006_ref_008","doi-asserted-by":"crossref","unstructured":"I. A. Shalimova and K. K. Sabelfeld,\nSolution to a stochastic Darcy equation by the polynomial chaos expansion,\nSib. Zh. Vychisl. Mat. 20 (2017), no. 3, 313\u2013327.","DOI":"10.1134\/S1995423917030077"},{"key":"2024083008370641169_j_mcma-2024-2006_ref_009","unstructured":"M. Springer,\nThe Algebra of Random Variables,\nJohn Wiley & Sons, New York, 1979."},{"key":"2024083008370641169_j_mcma-2024-2006_ref_010","doi-asserted-by":"crossref","unstructured":"S. Tennoe, G. Halnes and G. T. Einevoll,\nUncertainpy: A Python Toolbox for Uncertainty Quantification and Sensitivity Analysis, Computational Neuroscience,\nFront. Neuroinf. (2018), 10.3389\/fninf.2018.00049.","DOI":"10.1101\/274779"}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2006\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2006\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,30]],"date-time":"2024-08-30T08:37:18Z","timestamp":1725007038000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2006\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,18]]},"references-count":10,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,6,18]]},"published-print":{"date-parts":[[2024,9,1]]}},"alternative-id":["10.1515\/mcma-2024-2006"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2024-2006","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"type":"print","value":"0929-9629"},{"type":"electronic","value":"1569-3961"}],"subject":[],"published":{"date-parts":[[2024,6,18]]}}}