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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2019, Volume 25, Number 3, Pages 232–246
DOI: https://doi.org/10.21538/0134-4889-2019-25-3-232-246 (Mi timm1661) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the Construction of a Nonanticipating Selection of a Multivalued Mapping

D. A. Serkovab, A. G. Chentsovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
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DOI: https://doi.org/10.21538/0134-4889-2019-25-3-232-246
Abstract: We study the properties of multivalued mappings of general form with respect to the possibility of finding their nonanticipating selections. The property of nonanticipation is formulated for an arbitrary domain by specifying some family of “test” subsets. Sufficient conditions for the existence of a nonanticipating selection of a nonanticipating multivalued mapping are proposed: the values of the mapping must be nonempty compact sets, and the family of “test” subsets must be totally ordered with respect to inclusion. We illustrate the results by showing their applicability to the pursuit–evasion differential game in the form of P. Varaya and J. Lin.
Keywords: quasistrategy, nonanticipation, selection, topology.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations
This work was supported by the Presidium of the Russian Academy of Sciences within the project “Newest Methods of Mathematical Modeling in the Study of Nonlinear Dynamic Systems.”
Received: 15.05.2019
Revised: 19.06.2019
Accepted: 24.06.2019
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2020, Volume 309, Issue 1, Pages S125–S138
DOI: https://doi.org/10.1134/S008154382004015X
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: D. A. Serkov, A. G. Chentsov, “On the Construction of a Nonanticipating Selection of a Multivalued Mapping”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 3, 2019, 232–246; Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S125–S138
Citation in format AMSBIB
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\paper On the Construction of a Nonanticipating Selection of a Multivalued Mapping
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\vol 25
\issue 3
\pages 232--246
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\jour Proc. Steklov Inst. Math. (Suppl.)
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