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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 6, Pages 1030–1041
DOI: https://doi.org/10.31857/S0044466922060114 (Mi zvmmf11414) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Mathematical physics

Chernoff iterations as an averaging method for random affine transformations

R. Sh. Kalmetiev, Yu. N. Orlov, V. Zh. Sakbaev

Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia
Citations (8)
DOI: https://doi.org/10.31857/S0044466922060114
Abstract: For functions defined on a finite-dimensional vector space, we study compositions of their independent random affine transformations that represent a noncommutative analogue of random walks. Conditions on iterations of independent random affine transformations are established that are sufficient for convergence to a group solving the Cauchy problem for an evolution equation of shift along the averaged vector field and sufficient for convergence to a semigroup solving the Cauchy problem for the Fokker–Planck equation. Numerical estimates for the deviation of random iterations from solutions of the limit problem are presented. Initial-boundary value problems for differential equations describing the evolution of functionals of limit random processes are formulated and studied.
Key words: random linear operator, operator-valued random process, law of large numbers Fokker–Planck equation.
Received: 02.12.2021
Revised: 27.12.2021
Accepted: 15.01.2022
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 6, Pages 996–1006
DOI: https://doi.org/10.1134/S0965542522060100
Bibliographic databases:
Document Type: Article
UDC: 517.63
Language: Russian
Citation: R. Sh. Kalmetiev, Yu. N. Orlov, V. Zh. Sakbaev, “Chernoff iterations as an averaging method for random affine transformations”, Zh. Vychisl. Mat. Mat. Fiz., 62:6 (2022), 1030–1041; Comput. Math. Math. Phys., 62:6 (2022), 996–1006
Citation in format AMSBIB
\Bibitem{KalOrlSak22}
\by R.~Sh.~Kalmetiev, Yu.~N.~Orlov, V.~Zh.~Sakbaev
\paper Chernoff iterations as an averaging method for random affine transformations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 6
\pages 1030--1041
\mathnet{http://mi.mathnet.ru/zvmmf11414}
\crossref{https://doi.org/10.31857/S0044466922060114}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4452830}
\elib{https://elibrary.ru/item.asp?id=48506079}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 6
\pages 996--1006
\crossref{https://doi.org/10.1134/S0965542522060100}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf11414
  • https://www.mathnet.ru/eng/zvmmf/v62/i6/p1030
    • This publication is cited in the following 8 articles:
    1. R. Sh. Kalmetev, Yu. N. Orlov, V. Zh. Sakbaev, “Generalized Coherent States and Random Shift Operators”, Proc. Steklov Inst. Math., 324 (2024), 115–122  mathnet  crossref  crossref  mathscinet  zmath
    2. Oleg E. Galkin, Ivan D. Remizov, “Upper and lower estimates for rate of convergence in the Chernoff product formula for semigroups of operators”, Isr. J. Math., 2024  crossref
    3. R. Sh. Kalmetev, “Usrednenie po Chernovu lineinykh differentsialnykh uravnenii”, Preprinty IPM im. M. V. Keldysha, 2023, 010, 12 pp.  mathnet  crossref
    4. R. Sh. Kalmetev, “Approksimatsiya reshenii mnogomernogo uravneniya Kolmogorova s pomoschyu iteratsii Feinmana-Chernova”, Preprinty IPM im. M. V. Keldysha, 2023, 021, 15 pp.  mathnet  crossref
    5. R. Sh. Kalmetev, Yu. N. Orlov, V. Zh. Sakbaev, “Averaging of random affine transformations of functions domain”, Ufa Math. J., 15:2 (2023), 55–64  mathnet  crossref
    6. K. A. Dragunova, N. Nikbakht, I. D. Remizov, “Chislennoe issledovanie skorosti skhodimosti chernovskikh approksimatsii k resheniyam uravneniya teploprovodnosti”, Zhurnal SVMO, 25:4 (2023), 255–272  mathnet  crossref
    7. R. Sh. Kalmetev, Yu. N. Orlov, V. Zh. Sakbaev, “Quantum Decoherence via Chernoff Averages”, Lobachevskii J Math, 44:6 (2023), 2044  crossref
    8. K. Yu. Zamana, V. Zh. Sakbaev, “Compositions of independent random operators and related differential equations”, Keldysh Institute preprints, 2022, 49–23  mathnet  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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