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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 10, Pages 86–91
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This article is cited in 8 scientific papers (total in 8 papers)
Brief communications
On the law of large numbers for compositions of independent random semigroups
V. Zh. Sakbaev
Steklov Mathematical Institute of Russian Academy of Sciences,
8 Gubkin str., Moscow, 119991 Russia
Abstract:
We study random linear operators in Banach spaces and random one-parameter semigroups of such operators. For compositions of independent random semigroups of linear operators in the Hilbert space we obtain sufficient conditions for fulfilment of the law of large numbers and give examples of its violation.
Keywords:
law of large numbers, random map, random semigrop, Chernoff theorem.
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:10, 72–76
Bibliographic databases:
   
UDC:
517.98+519.2
Presented by the member of Editorial Board: А. М. Бикчентаев
Received: 24.03.2016
Citation:
V. Zh. Sakbaev, “On the law of large numbers for compositions of independent random semigroups”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 10, 86–91; Russian Math. (Iz. VUZ), 60:10 (2016), 72–76
Citation in format AMSBIB
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Citing articles on Google Scholar:
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This publication is cited in the following articles:
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Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Feynman formulas for nonlinear evolution equations”, Dokl. Math., 96:3 (2017), 574–577
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I. V. Volovich, V. Zh. Sakbaev, “On quantum dynamics on $C^*$-algebras”, Proc. Steklov Inst. Math., 301 (2018), 25–38
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V. Zh. Sakbaev, O. G. Smolyanov, “Feynman calculus for random operator-valued functions and their applications”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 160, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2018, 373–383
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V. Zh. Sakbaev, “Averaging of random flows of linear and nonlinear maps”, European Conference-Workshop Nonlinear Maps and Applications, Journal of Physics Conference Series, 990, IOP Publishing Ltd, 2018, 012012
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V. Zh. Sakbaev, “Polugruppy preobrazovanii prostranstva funktsii, kvadratichno integriruemykh po translyatsionno invariantnoi mere na banakhovom prostranstve”, Kvantovaya veroyatnost, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 151, VINITI RAN, M., 2018, 73–90
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D. V. Zavadsky, V. Zh. Sakbaev, “Diffusion on a Hilbert Space Equipped with a Shift- and Rotation-Invariant Measure”, Proc. Steklov Inst. Math., 306 (2019), 102–119
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Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Feynman Formulas and the Law of Large Numbers for Random One-Parameter Semigroups”, Proc. Steklov Inst. Math., 306 (2019), 196–211
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V. M. Busovikov, V. Zh. Sakbaev, “Sobolev spaces of functions on a Hilbert space endowed with a translation-invariant measure and approximations of semigroups”, Izv. Math., 84:4 (2020), 694–721
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