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

This article is cited in 3 scientific papers (total in 3 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


Full text: PDF file (182 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:10, 72–76

Bibliographic databases:

Document Type: Article
UDC: 517.98+519.2
Presented by the member of Editorial Board: A. M. Bikchentaev
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

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    Citing articles on Google Scholar: Russian citations, English citations
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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  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
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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