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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 10, Pages 86–91 (Mi ivm9169)  

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.

Funding Agency Grant Number
Russian Science Foundation 14-11-00687

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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
\by V.~Zh.~Sakbaev
\paper On the law of large numbers for compositions of independent random semigroups
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 10
\pages 86--91
\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 10
\pages 72--76

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    This publication is cited in the following articles:
    1. Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Feynman formulas for nonlinear evolution equations”, Dokl. Math., 96:3 (2017), 574–577  crossref  mathscinet  zmath  isi  elib  scopus
    2. I. V. Volovich, V. Zh. Sakbaev, “On quantum dynamics on $C^*$-algebras”, Proc. Steklov Inst. Math., 301 (2018), 25–38  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. 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  mathnet
    4. 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  crossref  mathscinet  isi  scopus
    5. 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  mathnet  mathscinet
    6. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    7. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    8. 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  mathnet  crossref  crossref  mathscinet  isi
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