Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University1006310.18287/2541-7525-2021-27-1-74-80Research ArticlePROBLEMS OF DIFFERENTIAL AND TOPOLOGICAL DIAGNOSTICS. PART 6. STATISTICAL SOLVING OF THE PROBLEM OF DIFFERENTIAL DIAGNOSTICSShamolinM. V.<p>Doctor of Physical and Mathematical Sciences, professor, leading researcher of the Institute of Mechanics, academic of the Russian Academy of Natural Sciences</p>shamolin@rambler.ruhttps://orcid.org/0000-0002-9534-0213Institute of Mechanics, Lomonosov Moscow State University1904202127174801502202215022022Copyright © 2021, Shamolin M.V.2021<p>Proposed work is the sixth work of the cycle on differential and topological diagnostics. It is shown that the diagnostics in the case of trajectorial measurements corrupted by noise, which is a stochastic process of the normal white noise type with zero mean value and bounded spectrum, can be performed by using the diagnostic algorithms obtained in [5], i.e., the results of this section remain valid even in this rather general case; moreover, the diagnostic functional, which was introduced in the theorem of [5] a priori, is now obtained a posteriori.</p>задача диагностированияалгоритмы диагностированиястатистическое решениеdiagnostic problemdiagnostic algorithmsstatistical solving[Shamolin M.V. Problems of differential and topological diagnostics. Part 1. Motion equations and classification of malfunctions. Vestnik Samarskogo universiteta. Estestvennonauchnaia seriia =Vestnik of Samara University. Natural Science Series, 2019, vol. 25, no. 1, pp. 32–43. Available at: http://doi.org/10.18287/2541-7525-2019-25-1-32-43. (In Russ.)][Shamolin M.V. 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Problems of differential and topological diagnostics. Part 5. The case of trajectorial measurements with error. Vestnik Samarskogo universiteta. Estestvennonauchnaia seriia = Vestnik of Samara University. Natural Science Series, 2020, vol. 26, no. 3, pp. 30–39. DOI: http://doi.org/10.18287/2541-7525-2020-26-3-30-39. (In Russ.)][Borisenok I.T., Shamolin M.V. Solution of a problem of differential diagnostics. Fundamental and Applied Mathematics, 1999, vol. 5, no. 3, pp. 775–790. Available at: http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=fpm&paperid=401&option_lang=rus. (In Russ.)][Shamolin M.V. Certain problems of differential and topological diagnostics. 2nd edition, revised and enlarged. Moscow: Ekzamen, 2007. Available at: http://eqworld.ipmnet.ru/ru/library/books/Shamolin2007-2ru.pdf. (In Russ.)][Shamolin M.V. Foundations of Differential and Topological Diagnostics. Journal of Mathematical Sciences, 2003, vol. 114, no. 1, pp. 976–1024. 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